5,647 results on '"Integral inequalities"'
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102. A HILBERT-TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITY WITH THE KERNEL OF A HYPERBOLIC COSECANT FUNCTION.
- Author
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LIU, YINGDI and LIU, QIONG
- Subjects
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FRACTIONAL integrals , *HYPERBOLIC functions , *FRACTIONAL calculus , *INTEGRAL inequalities , *FRACTALS - Abstract
By using Yang's local fractional calculus theory, the method of weight function, and real-analysis techniques in the fractal set, a general Hilbert-type local fractional integral inequality with the kernel of a hyperbolic cosecant function is established. The necessary and sufficient condition for the constant factor of the general Hilbert-type local fractional integral inequality to be the best possible is discovered. Furthermore, two equivalent inequalities with the best constant factors were obtained. [ABSTRACT FROM AUTHOR]
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- 2024
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103. ON GENERAL LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED H-PREINVEX FUNCTIONS ON YANG'S FRACTAL SETS.
- Author
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ZHANG, YONG and SUN, WENBING
- Subjects
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FRACTIONAL integrals , *FRACTALS , *GENERALIZED integrals , *NUMERICAL functions , *INTEGRAL inequalities , *NUMERICAL integration - Abstract
In this paper, based on Yang's fractal theory, the Hermite–Hadamard's inequalities for generalized h -preinvex function are proved. Then, using the local fractional integral identity proposed by Sun [Some local fractional integral inequalities for generalized preinvex functions and applications to numerical quadrature, Fractals 27(5) (2019) 1950071] as auxiliary function, some parameterized local fractional integral inequalities for generalized h -preinvex functions are established. For the special cases of the parameters, some generalized Simpson-type, midpoint-type and trapezoidal inequalities are established. Finally, some applications of these inequalities in numerical integration are proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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104. Fractional integral inequalities and error estimates of generalized mean differences.
- Author
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Samraiz, Muhammad, Ghaffar, Muhammad Tanveer, Naheed, Saima, and Vivas-Cortez, Miguel
- Subjects
FRACTIONAL integrals ,INTEGRAL inequalities ,MATHEMATICS ,INTEGRALS - Abstract
In this research, we focus on a novel class of mean inequalities involving Riemann-Liouville fractional integrals. We employ these integrals to investigate various fundamental identities that help us to explore mean inequalities. By utilizing a generalized concept of convexity, we establish a unique set of these problems. To ensure the accuracy of our findings, we generate 2D and 3D graphs accompanied by corresponding numerical data using specific functions, effectively illustrating the inequalities. Furthermore, it is easy to observe that some known results from previous studies manifest as special cases of our primary outcomes. This approach enables us to substantiate the validity of our findings and strengthen our conclusions. The connection of the main finding with the context of statistics and mathematics is provided, playing a significant role in addressing real-life problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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105. Sawtooth-characteristic-based free matrix integral inequality and its application to sampled-data systems.
- Author
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Zhang, Ying, He, Yong, and Shangguan, Xing-Chen
- Subjects
INTEGRAL inequalities ,DISCRETE-time systems ,MATRIX inequalities ,LINEAR matrix inequalities ,STABILITY criterion ,ELECTRICITY markets - Abstract
The focus of this article is to present a sawtooth-characteristic-based free-matrix integral inequality and to discuss its application to sampled-data systems (SDSs). Firstly, the free matrix, which is associated with the sawtooth characteristic of the input delay, is presented and incorporated into the integral inequality. In the development of inequality techniques, this is the first time that a free matrix has been associated with the sawtooth characteristic. On this basis, a corresponding sawtooth-characteristic-based free-matrix integral inequality is established, enabling estimation of the integral quadratic terms of the Lyapunov–Krasovskii functional (LKF) derivative. To overcome the challenges posed by second-order terms resulting from the proposed integral inequality, augmented system variables associated with the sawtooth characteristic are also introduced. Thus, the complicated calculation arising from second-order terms and the conservatism caused by the quadratic estimation of the LKF can be avoided. Finally, through the utilization of the sawtooth-characteristic-based free-matrix integral inequality, stability criteria with less conservatism are derived for the SDSs in the form of linear matrix inequalities. The superiority of the proposed approach is illustrated through two numerical examples and a simplified sampled-data based power market. • A sawtooth-characteristic-based free-matrix integral inequality is proposed for the first time. The novelty of this inequality technique is that the commonly used constant free matrix is set to be input delay, i.e., d k 1 (t) -dependent matrix. This is the first time that a free matrix has been associated with the sawtooth characteristic. • Some augmented system variables associated with the input delay d k 1 (t) and the corresponding free-weighting-matrix are introduced to reduce the high-order terms of d k 1 (t). Thanks to the introduction of augmented system variables, the complicated calculation arising from d k 1 (t) 2 -related terms as well as the conservatism caused by the quadratic estimation of the LKF, can be avoided. Meanwhile, some high-order LKF that have been abandoned by scholars because of cumbersome calculations can also be selected as LKF candidates without quadratic treatment. • The proposed sawtooth-characteristic-based free-matrix integral inequality is employed for sampled-data system. The integral quadratic terms of the LKF derivative can be converted into some sawtooth-characteristic-dependent terms by the proposed integral inequality, and less conservative stability criteria for SDSs are obtained. [ABSTRACT FROM AUTHOR]
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- 2024
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106. Novel inequalities for subadditive functions via tempered fractional integrals and their numerical investigations.
- Author
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Kashuri, Artion, Sahoo, Soubhagya Kumar, Mohammed, Pshtiwan Othman, Al-Sarairah, Eman, and Chorfi, Nejmeddine
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FRACTIONAL integrals ,INTEGRAL inequalities ,INTEGRAL operators ,INTEGRALS - Abstract
In this paper, we proposed some new integral inequalities for subadditive functions and the product of subadditive functions. Additionally, a novel integral identity was established and a number of inequalities of the Hermite-Hadamard type for subadditive functions pertinent to tempered fractional integrals were proved. Finally, to support the major results, we provided several examples of subadditive functions and corresponding graphs for the newly proposed inequalities. [ABSTRACT FROM AUTHOR]
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- 2024
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107. A generalization of convexity via an implicit inequality.
- Author
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Aydi, Hassen, Samet, Bessem, and De la Sen, Manuel
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GENERATING functions ,GENERALIZATION ,INTEGRAL inequalities ,CONVEXITY spaces - Abstract
We unified several kinds of convexity by introducing the class A
ζ, w ([0; 1] × I²) of (ζ, w)-admissible functions F: [0, 1] × I × I → R. Namely, we proved that most types of convexity from the literature generate functions F ∈ Aζ, w ([0, 1] × I²) for some ζ ∈ C([0, 1]) and w ∈ C¹(I) with w(I) ⊂ I and w0 > 0. We also studied some properties of (ζ, w)-admissible functions and established some integral inequalities that unify various Hermite-Hadamard-type inequalities from the literature. [ABSTRACT FROM AUTHOR]- Published
- 2024
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108. Further improvements of the Jensen inequality in the integral sense by virtue of 6-convexity along with applications.
- Author
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Sohail, Asadullah, Khan, Muhammad Adil, Nasr, Emad Abouel, and Xiaoye Ding
- Subjects
JENSEN'S inequality ,INTEGRAL inequalities ,INFORMATION theory - Abstract
The Jensen inequality is of fundamental importance because of its influential and interesting consequences. In recent years, the Jensen inequality has been supposed to be the most engaging source for research. We present interesting improvements to the continuous version of Jensen's inequality through the application of the concept of 6-convexity. For real visualization and comparison to other results, some numerical experiments were provided. With the aid of the acquired results, improvements for the Hermite-Hadamard and Hölder inequalities were presented. Some relationships between the means were granted as applications of established improvements. In addition, some estimations of the Csiszár divergence and its associated cases were received as further applications of the obtained results. The major techniques employed in formulating the proposed improvements included the Jensen inequality and the concept of convexity. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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109. Some new properties of geometrically-convex functions.
- Author
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Furuichi, Shigeru, Minculete, Nicuşor, Moradi, Hamid Reza, and Sababheh, Mohammad
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HYPERBOLIC functions ,EXPONENTIAL functions ,CONVEX functions ,INTEGRAL inequalities - Abstract
The class of geometrically convex functions is a rich class that contains some important functions. In this paper, we further explore this class and present many interesting new properties, including fundamental inequalities, supermultiplicative type inequalities, Jensen-Mercer inequality, integral inequalities, and refined forms. The obtained results extend some celebrated results from the context of convexity to geometric convexity, with interesting applications to numerical inequalities for the hyperbolic and exponential functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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110. Application of the Auxiliary Function Method to the Search for the Global Minimum of Functions of Many Variables.
- Author
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Salavatovna, Tutkusheva Zhailan and Toktarovich, Otarov Khassen
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LEBESGUE integral ,FUNCTION spaces ,CONVEX functions ,INTEGRAL inequalities ,TEST design - Abstract
In early works, we presented a new economical and effective method for finding the global optimum of a function of many variables, which was conditionally called the auxiliary function method. The essence of the method is that a multi-extremal and multivariable objective function is transformed into a convex function $g_m(F, \alpha)$ of one variable, which is the Lebesgue integral over a compact where the objective function is considered: $g_m(F, \alpha)=\int_E[|F(x)-\alpha|-F(x)+\alpha]^m d \mu$, $m \in N$. The function $g_m(F, \alpha)$ was called the auxiliary function. In early works, the properties of the auxiliary function and the algorithm of the new method were studied, the convergence of the method was proven, and computational experiments were carried out with multiextremal functions in three-dimensional space. Based on these results and in order to demonstrate the advantages of using the auxiliary function method, this paper considers the problem of finding global minima of objective functions in a four-dimensional space constructed on the basis of hyperbolic and exponential potentials and conducts a comparative analysis of the results obtained. In this work, as a result of completed computational experiments on test functions in three-dimensional and four-dimensional space, where auxiliary functions with different values of the degree $m \in N$ were expanded, important conclusions were obtained and proven. As a result, the change in the auxiliary function depending on its degree m is clearly shown. This result provides even more opportunities to improve the efficiency of the constructed method. Next, you can set up first- and second-order methods to find the "oldest" zero auxiliary function. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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111. Observer-based fuzzy integral sliding mode control for bilateral teleoperation systems with time-varying delays.
- Author
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Janani, K., Baranitha, R., Lim, Chee Peng, and Rakkiyappan, R.
- Subjects
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FUZZY integrals , *SLIDING mode control , *REMOTE control , *TIME-varying systems , *INTEGRAL inequalities , *ADAPTIVE fuzzy control , *FUZZY neural networks , *MATRIX inequalities , *LINEAR matrix inequalities - Abstract
This paper aims to examine the stability and tracking performance of a bilateral teleoperation system. The Takagi–Sugeno fuzzy method is utilized, through which the nonlinear master–slave dynamics is converted as a fuzzy-based system. The state observers are designed for the linearized fuzzy teleoperation systems, and the corresponding estimation errors are formulated. Importantly, a novel observer-based fuzzy integral sliding mode control is developed by deliberately introducing the delay term into the sliding surfaces. As such, advanced delay-product type of Lyapunov–Krasovskii functionals are constructed for the augmented state vectors, in order to acquire the additional delay information. In addition, the Wirtinger-based integral inequality along with an extended reciprocally convex matrix inequality is applied to the Lyapunov derivatives to establish the delay-dependent stability conditions. Numerical results are provided to demonstrate efficacy of the developed control mechanism. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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112. On the multiparameterized fractional multiplicative integral inequalities
- Author
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Mohammed Bakheet Almatrafi, Wedad Saleh, Abdelghani Lakhdari, Fahd Jarad, and Badreddine Meftah
- Subjects
Multiparameterized identity ,Integral inequalities ,Fractional multiplicative integral ,Multiplicative s-convexity ,Mathematics ,QA1-939 - Abstract
Abstract We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus.
- Published
- 2024
- Full Text
- View/download PDF
113. A generalization of convexity via an implicit inequality
- Author
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Hassen Aydi, Bessem Samet, and Manuel De la Sen
- Subjects
convexity ,implicit inequality ,$ (\zeta, w) $-admissible functions ,integral inequalities ,hermite-hadamard-type inequalities ,Mathematics ,QA1-939 - Abstract
We unified several kinds of convexity by introducing the class $ \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ of $ (\zeta, w) $-admissible functions $ F: [0, 1]\times I\times I\to \mathbb{R} $. Namely, we proved that most types of convexity from the literature generate functions $ F\in \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ for some $ \zeta\in C([0, 1]) $ and $ w\in C^1(I) $ with $ w(I)\subset I $ and $ w' > 0 $. We also studied some properties of $ (\zeta, w) $-admissible functions and established some integral inequalities that unify various Hermite-Hadamard-type inequalities from the literature.
- Published
- 2024
- Full Text
- View/download PDF
114. On parameterized inequalities for fractional multiplicative integrals
- Author
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Zhu Wen Sheng, Meftah Badreddine, Xu Hongyan, Jarad Fahd, and Lakhdari Abdelghani
- Subjects
parametrized identity ,integral inequalities ,fractional multiplicative integral ,multiplicative s-convexity ,26a33 ,26a51 ,26d10 ,26d15 ,Mathematics ,QA1-939 - Abstract
In this article, we present a one-parameter fractional multiplicative integral identity and use it to derive a set of inequalities for multiplicatively ss-convex mappings. These inequalities include new discoveries and improvements upon some well-known results. Finally, we provide an illustrative example with graphical representations, along with some applications to special means of real numbers within the domain of multiplicative calculus.
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- 2024
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115. Generalized strongly n-polynomial convex functions and related inequalities
- Author
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Serap Özcan, Mahir Kadakal, İmdat İşcan, and Huriye Kadakal
- Subjects
Convex function ,Generalized strongly n-polynomial convex function ,Hermite–Hadamard inequality ,Hölder-İşcan inequality ,Integral inequalities ,Analysis ,QA299.6-433 - Abstract
Abstract This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided.
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- 2024
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116. Midpoint-type integral inequalities for (s, m)-convex functions in the third sense involving Caputo fractional derivatives and Caputo–Fabrizio integrals
- Author
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Khuram Ali Khan, Iqra Ikram, Ammara Nosheen, Ndolane Sene, and Y. S. Hamed
- Subjects
Convex function ,integral inequalities ,Caputo fractional derivatives ,Caputo–Fabrizio integral operators ,39B62 ,39B05 ,Mathematics ,QA1-939 ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
In this study, midpoint-type integral inequalities for [Formula: see text]-convex function in the third sense, involving Caputo fractional derivatives and Caputo–Fabrizio integral operators, are demonstrated. Inequalities, containing Caputo–Fabrizio integral operators for functions, whose derivatives are [Formula: see text]-convex function in the third sense, are also established. This article utilized [Formula: see text]-convex function in the third sense to generalized midpoint-type integral inequalities which give more sharp inequalities.
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- 2024
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117. Parametrized multiplicative integral inequalities.
- Author
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Frioui, Assia, Meftah, Badreddine, Shokri, Ali, Lakhdari, Abdelghani, and Mukalazi, Herbert
- Subjects
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INTEGRAL inequalities , *REAL numbers , *CALCULUS , *INTEGRALS - Abstract
In this paper, we introduce a biparametrized multiplicative integral identity and employ it to establish a collection of inequalities for multiplicatively convex mappings. These inequalities encompass several novel findings and refinements of established results. To enhance readers' comprehension, we offer illustrative examples that highlight appropriate choices of multiplicatively convex mappings along with graphical representations. Finally, we demonstrate the applicability of our results to special means of real numbers within the realm of multiplicative calculus. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
118. Improved stability and stabilisation conditions of uncertain switched time-delay systems.
- Author
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Liu, Cai, Liu, Fang, Yang, Tianqing, and Liu, Kangzhi
- Subjects
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INTEGRAL inequalities , *LINEAR matrix inequalities , *HOPFIELD networks , *RIVER pollution , *STABILITY criterion , *DYNAMICAL systems - Abstract
This article is concerned with the stability and stabilisation of switched time-delay systems (STDSs) with exponential uncertainty. Based on the Hurwitz convex combination and the energy attenuation principle, an improved state-dependent switching strategy is proposed, which switches to the next modes to obey the minimum energy. This approach fully considers the system dynamic of subsystems, which is more general. Considering the complex switching and delay dynamics, a mode-dependent Lyapunov–Krasovskii functional (LKF) that contains a triple integral term is constructed. The generalised free-matrix-based integral inequality (GFMBII) is used to estimate the integral terms in the derivative of the LKF, and an improved delay-dependent stability criterion is established in the form of linear matrix inequalities (LMIs). Further, to guarantee the stability of the STDSs with a large time-varying delay, a controller that considers the time delay and the exponential uncertainty is designed. Under this controller, a less conservative delay-dependent robust stabilisation criterion for STDSs with exponential uncertainty is established. The validity of the proposed methods is validated by two numerical examples and an application in river pollution control. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
119. On strongly generalized convex stochastic processes.
- Author
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Sharma, Nidhi, Mishra, Rohan, and Hamdi, Abdelouahed
- Subjects
- *
STOCHASTIC processes , *CONVEX functions , *INTEGRAL inequalities - Abstract
In this paper, we introduce the notion of strongly generalized convex functions which is called as strongly η-convex stochastic processes. We prove the Hermite-Hadamard, Ostrowski type inequality, and obtain some important inequalities for above processes. Some previous results are special cases of the results obtained in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
120. Hyers–Ulam Stability of 2 D -Convex Mappings and Some Related New Hermite–Hadamard, Pachpatte, and Fejér Type Integral Inequalities Using Novel Fractional Integral Operators via Totally Interval-Order Relations with Open Problem.
- Author
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Afzal, Waqar, Breaz, Daniel, Abbas, Mujahid, Cotîrlă, Luminiţa-Ioana, Khan, Zareen A., and Rapeanu, Eleonora
- Subjects
- *
INTEGRAL operators , *FRACTIONAL integrals , *INTEGRAL inequalities , *LINEAR orderings - Abstract
The aim of this paper is to introduce a new type of two-dimensional convexity by using total-order relations. In the first part of this paper, we examine the Hyers–Ulam stability of two-dimensional convex mappings by using the sandwich theorem. Our next step involves the development of Hermite–Hadamard inequality, including its weighted and product forms, by using a novel type of fractional operator having non-singular kernels. Moreover, we develop several nontrivial examples and remarks to demonstrate the validity of our main results. Finally, we examine approximate convex mappings and have left an open problem regarding the best optimal constants for two-dimensional approximate convexity. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
121. ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS.
- Author
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PENG, YU and DU, TINGSONG
- Subjects
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CALCULUS , *FRACTIONAL integrals , *FRACTIONAL calculus , *INTEGRAL inequalities - Abstract
In this paper, we propose a fresh conception about convexity, known as the multiplicative (s , P) -convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the ∗ differentiable (s , P) -convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and Newton-type inequalities. To further verify the validity of our primary outcomes, we give a few numerical examples. As applications, we proffer a number of inequalities of multiplicative type in special means as well. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
122. Improved dissipativity‐based analysis and synthesis of T‐S fuzzy systems with aperiodic memory sampled‐data controllers via an augmented looped‐functional.
- Author
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Liu, Yun‐Fan, Zhang, Chuan‐Ke, Fan, Yu‐Long, Chen, Wen‐Hu, and Shangguan, Xing‐Chen
- Subjects
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FUZZY systems , *INTEGRAL inequalities , *MEMORY , *TELECOMMUNICATION systems , *TRUCK trailers - Abstract
The dissipativity‐based analysis and synthesis issues of Takagi‐Sugeno (T‐S) fuzzy systems by applying aperiodic memory sampling control are investigated in this paper. Compared with the more conservative dissipative conditions and controller design methods proposed in the past based on Lyapunov theory, the main purpose of this paper is to obtain a less conservative dissipative criterion and devise an aperiodic memory sampled‐data controller. Firstly, the sampling controller is assumed to work in aperiodic sample mode, and the time delay in the communication network is considered. Next, an augmented delay‐product‐type looped‐functional is proposed such that the whole information of sampling and delay, which has not been studied before, is well taken into account. A new dissipative criterion and an aperiodic sampled‐data control strategy are proposed by applying free‐matrix‐based integral inequalities consequently. Finally, a truck‐trailer system is implemented to elaborate the availability and the merit of the designed strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
123. Blow up, growth, and decay of solutions for a class of coupled nonlinear viscoelastic Kirchhoff equations with distributed delay and variable exponents.
- Author
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Boulaaras, Salah, Choucha, Abdelbaki, Ouchenane, Djamel, and Jan, Rashid
- Subjects
- *
EXPONENTS , *EQUATIONS , *DELAY differential equations , *LYAPUNOV exponents , *INTEGRAL inequalities , *BLOWING up (Algebraic geometry) , *PARTIAL differential equations - Abstract
In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 . [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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124. On the multiparameterized fractional multiplicative integral inequalities.
- Author
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Almatrafi, Mohammed Bakheet, Saleh, Wedad, Lakhdari, Abdelghani, Jarad, Fahd, and Meftah, Badreddine
- Subjects
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FRACTIONAL integrals , *INTEGRAL inequalities , *REAL numbers , *VISUAL aids , *CALCULUS - Abstract
We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
125. ON HARDY-TYPE INEQUALITIES AS AN INTELLECTUAL ADVENTURE FOR 100 YEARS.
- Author
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Persson, Lars-Erik and Samko, Natasha
- Subjects
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INTEGRAL inequalities , *ADVENTURE & adventurers , *CIRCLE , *CONVEXITY spaces - Abstract
We describe some chosen ideas and results for more than 100 years prehistory and history of the remarkable development concerning Hardy-type inequalities. In particular, we present a newer convexity approach, which we believe could partly have changed this development if Hardy had discovered it. In order to emphasize the current very active interest in this subject, we finalize by presenting some examples of the recent results, which we believe have potential not only to be of interest for a broad audience from a historical perspective, but also to be useful in various applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
126. Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators.
- Author
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Hao, Zhiwei, Li, Libo, Long, Long, and Weisz, Ferenc
- Subjects
- *
FRACTIONAL integrals , *INTEGRAL inequalities , *INTEGRAL operators , *FUNCTION spaces , *HARDY spaces , *MARTINGALES (Mathematics) - Abstract
Let 0 < q ≤ ∞ , b be a slowly varying function and Φ : [ 0 , ∞) ⟶ [ 0 , ∞) be an increasing function with Φ (0) = 0 and lim r → ∞ Φ (r) = ∞ . In this paper, we introduce a new class of function spaces L Φ , q , b which unify and generalize the Lorentz-Karamata spaces with Φ (t) = t p and the Orlicz-Lorentz spaces with b ≡ 1 . Based on the new spaces, we introduce five new Hardy spaces containing martingales, the so-called Orlicz-Lorentz-Karamata Hardy martingale spaces and then develop a theory of these martingale Hardy spaces. To be precise, we first investigate several properties of Orlicz-Lorentz-Karamata spaces and then present Doob's maximal inequalities by using Hardy's inequalities. The characterization of these Hardy martingale spaces are constructed via the atomic decompositions. As applications of the atomic decompositions, martingale inequalities and the relation of the different martingale Hardy spaces are presented. The dual theorems and a new John-Nirenberg type inequality for the new framework are also established. Moreover, we study the boundedness of fractional integral operators on Orlicz-Lorentz-Karamata Hardy martingale spaces. The results obtained here generalize the previous results for Lorentz-Karamata Hardy martingale spaces as well as for Orlicz-Lorentz Hardy martingales spaces. Especially, we remove the condition that b is non-decreasing as in [38-39] and the condition q Φ - 1 < 1 / q in [24], respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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127. A Pexider equation containing the aritmetic mean.
- Author
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Kiss, Tibor
- Subjects
- *
FUNCTIONAL equations , *EQUATIONS , *ARITHMETIC mean , *INTEGRAL inequalities - Abstract
In this paper we determine the solutions (φ , f 1 , f 2) of the Pexider functional equation φ ( x + y 2) (f 1 (x) - f 2 (y)) = 0 , (x , y) ∈ I 1 × I 2 , where I 1 and I 2 are nonempty open subintervals. Special cases of the above equation regularly arise in problems with two-variable means. We show that, under a rather weak regularity condition, the coordinate-functions of a typical solution of the equation are constant over several subintervals of their domain. The regularity condition in question will be that the set of zeros of φ is closed. We also discuss particular solutions where this condition is not met. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
128. Refinements of discrete and integral Jensen inequalities with Jensen's gap.
- Author
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Horváth, László
- Subjects
- *
JENSEN'S inequality , *INTEGRAL inequalities , *INFORMATION theory - Abstract
Motivated by a paper of Dragomir, we give new refinements for both discrete and integral Jensen inequalities using the Jensen's gap. As applications, we give refinements of various inequalities verifiable by Jensen's inequality. Topics covered: norms, quasi-arithmetic means, Hölder's inequality and f-divergences in information theory. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
129. Inequalities of Ostrowski Type for Functions Whose Derivative Module Is Relatively Convex on Time Scales.
- Author
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Rezk, Haytham M., Saied, Ahmed I., Ali, Maha, AlNemer, Ghada, and Zakarya, Mohammed
- Subjects
- *
INTEGRAL inequalities , *CONVEX functions - Abstract
In this article, we discuss several novel generalized Ostrowski-type inequalities for functions whose derivative module is relatively convex in time scales calculus. Our core findings are proved by using the integration by parts technique, Hölder's inequality, and the chain rule on time scales. These derived inequalities expand the existing literature, enriching specific integral inequalities within this domain. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
130. Weak Sharp Type Solutions for Some Variational Integral Inequalities.
- Author
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Treanţă, Savin and Saeed, Tareq
- Subjects
- *
INTEGRAL inequalities , *INTEGRALS - Abstract
Weak sharp type solutions are analyzed for a variational integral inequality defined by a convex functional of the multiple integral type. A connection with the sufficiency property associated with the minimum principle is formulated, as well. Also, an illustrative numerical application is provided. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
- View/download PDF
131. Further Fractional Hadamard Integral Inequalities Utilizing Extended Convex Functions.
- Author
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Almoneef, Areej A., Barakat, Mohamed A., and Hyder, Abd-Allah
- Subjects
- *
FRACTIONAL integrals , *CONVEX functions , *INTEGRAL inequalities , *MATHEMATICAL analysis , *INTEGRAL operators - Abstract
This work investigates novel fractional Hadamard integral inequalities by utilizing extended convex functions and generalized Riemann-Liouville operators. By carefully using extended integral formulations, we not only find novel inequalities but also improve the accuracy of error bounds related to fractional Hadamard integrals. Our study broadens the applicability of these inequalities and shows that they are useful for a variety of convexity cases. Our results contribute to the advancement of mathematical analysis and provide useful information for theoretical comprehension as well as practical applications across several scientific directions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
132. Error Bounds for Fractional Integral Inequalities with Applications.
- Author
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Alqahtani, Nouf Abdulrahman, Qaisar, Shahid, Munir, Arslan, Naeem, Muhammad, and Budak, Hüseyin
- Subjects
- *
FRACTIONAL integrals , *INTEGRAL inequalities , *FRACTIONAL calculus , *DIFFERENTIABLE functions , *CONVEX functions , *MATRIX inequalities , *CONCAVE functions - Abstract
Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson's type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson's type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
133. Existence of Solutions for the Initial Value Problem with Hadamard Fractional Derivatives in Locally Convex Spaces.
- Author
-
Liu, Weiwei and Liu, Lishan
- Subjects
- *
INTEGRAL inequalities , *FRACTIONAL differential equations , *NONLINEAR differential equations , *DIFFERENTIAL operators , *INITIAL value problems , *NONLINEAR equations , *INTEGRAL equations - Abstract
In this paper, we investigate an initial value problem for a nonlinear fractional differential equation on an infinite interval. The differential operator is taken in the Hadamard sense and the nonlinear term involves two lower-order fractional derivatives of the unknown function. In order to establish the global existence criteria, we first verify that there exists a unique positive solution to an integral equation based on a class of new integral inequality. Next, we construct a locally convex space, which is metrizable and complete. On this space, applying Schäuder's fixed point theorem, we obtain the existence of at least one solution to the initial value problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
134. New Inequalities Using Multiple Erdélyi–Kober Fractional Integral Operators.
- Author
-
Tassaddiq, Asifa, Srivastava, Rekha, Alharbi, Rabab, Kasmani, Ruhaila Md, and Qureshi, Sania
- Subjects
- *
INTEGRAL operators , *INTEGRAL inequalities , *FRACTIONAL calculus , *FRACTIONAL integrals - Abstract
The role of fractional integral inequalities is vital in fractional calculus to develop new models and techniques in the most trending sciences. Taking motivation from this fact, we use multiple Erdélyi–Kober (M-E-K) fractional integral operators to establish Minkowski fractional inequalities. Several other new and novel fractional integral inequalities are also established. Compared to the existing results, these fractional integral inequalities are more general and substantial enough to create new and novel results. M-E-K fractional integral operators have been previously applied for other purposes but have never been applied to the subject of this paper. These operators generalize a popular class of fractional integrals; therefore, this approach will open an avenue for new research. The smart properties of these operators urge us to investigate more results using them. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
135. pq -Simpson's Type Inequalities Involving Generalized Convexity and Raina's Function.
- Author
-
Vivas-Cortez, Miguel, Baig, Ghulam Murtaza, Awan, Muhammad Uzair, and Brahim, Kamel
- Subjects
- *
CONVEXITY spaces , *INTEGRAL inequalities , *CONVEX functions - Abstract
This study uses Raina's function to obtain a new coordinated p q -integral identity. Using this identity, we construct several new p q -Simpson's type inequalities for generalized convex functions on coordinates. Setting p 1 = p 2 = 1 in these inequalities yields well-known quantum Simpson's type inequalities for coordinated generalized convex functions. Our results have important implications for the creation of post quantum mathematical frameworks. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
136. SOME INTEGRAL INEQUALITIES THROUGH TEMPERED FRACTIONAL INTEGRAL OPERATOR.
- Author
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GÜL, Erdal and YALÇIN, Abdüllatif
- Subjects
- *
INTEGRAL operators , *FRACTIONAL integrals , *INTEGRAL inequalities , *CONCAVE functions - Abstract
In this article, we adopt the tempered fractional integral operators to develop some novel Minkowski and Hermite-Hadamard type integral inequalities. Thus, we give several special cases of the integral inequalities for tempered fractional integrals obtained in the earlier works. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
137. Dynamic Event-Triggered Control for Delayed Nonlinear Markov Jump Systems under Randomly Occurring DoS Attack and Packet Loss.
- Author
-
Zhang, Haiyang, Chen, Huizhen, Xiong, Lianglin, and Zhang, Yi
- Subjects
- *
MARKOVIAN jump linear systems , *EXPONENTIAL stability , *DENIAL of service attacks , *RELIABILITY in engineering , *STABILITY criterion , *INTEGRAL inequalities - Abstract
This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attacks and packet loss. Firstly, the stochastic characteristics of DoS attacks and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of the systems. Then, by constructing a general common Lyapunov functional and combining it with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through two examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
138. Generalized n -Polynomial p -Convexity and Related Inequalities.
- Author
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Özcan, Serap and Cotîrlă, Luminiţa-Ioana
- Subjects
- *
MATHEMATICAL instruments , *ABSOLUTE value , *CONVEXITY spaces , *CONVEX functions , *INTEGRAL inequalities - Abstract
In this paper, we construct a new class of convex functions, so-called generalized n-polynomial p-convex functions. We investigate their algebraic properties and provide some relationships between these functions and other types of convex functions. We establish Hermite–Hadamard (H–H) inequality for the newly defined class of functions. Additionally, we derive refinements of H–H inequality for functions whose first derivatives in absolute value at certain power are generalized n-polynomial p-convex. When p = − 1 , our definition evolves into a new definition for the class of convex functions so-called generalized n-polynomial harmonically convex functions. The results obtained in this study generalize regarding those found in the existing literature. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
139. New fractal–fractional Simpson estimates for twice differentiable functions with applications.
- Author
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Butt, Saad Ihsan, Khan, Ahmad, and Tipurić-Spužević, Sanja
- Subjects
- *
DIFFERENTIABLE functions , *INTEGRAL inequalities , *FRACTALS , *INTEGRAL operators , *RANDOM variables , *WAVE equation - Abstract
In this article, we establish a new auxiliary identity on fractal sets for twice local differentiable function involving extended fractal integral operators. Testing this identity together with generalized fractal Hölder’s and Power-mean integral inequalities, we develop some new fractal–fractional Simpson’s type inequalities. Furthermore, we use modified Yang Hölder’s and Power-mean inequality to create new fractal estimates. We also give comparison analysis of bounds and show how the modified form of Yang Hölder’s and Powermean integral inequalities can result in improved lower upper bounds. We also provide concrete examples to examine the validity of obtain results numerically and also justify them by 2D and 3D graphical analysis. As implementations, we operate our findings to get new applications in form of ζ-type special means, moment of random variables and wave equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
140. A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS.
- Author
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SITTHIWIRATTHAM, THANIN, VIVAS-CORTEZ, MIGUEL, ALI, MUHAMMAD AAMIR, BUDAK, HÜSEYIN, and AVCI, İBRAHIM
- Subjects
- *
FRACTIONAL integrals , *INTEGRAL inequalities - Abstract
In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite–Hadamard–Mercer-type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of midpoint type, trapezoidal type, and Simpson's type for differentiable functions. Finally, we show the validation of the results with the help of some mathematical examples and their graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
141. SOME NEW TRAPEZOIDAL TYPE INEQUALITIES FOR STRONGLY GEOMETRIC-ARITHMETICALLY CONVEX FUNCTIONS.
- Author
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DEMÍREL, A. K.
- Subjects
CONVEX functions ,INTEGRAL inequalities ,ARITHMETIC functions - Abstract
This paper considers some preliminary conclusions of Fejér's integral inequality relevant to strongly geometric arithmetic convex functions that is a type of the class of convex functions and also a mapping to produce a novel trapezoidal form. This mapping is used to derive new theorems and results. By utilization these, some applications were given. [ABSTRACT FROM AUTHOR]
- Published
- 2024
142. On Hermite-Hadamard type inequalities for co-ordinated convex function via conformable fractional integrals.
- Author
-
Kiriş, Mehmet Eyüp, Vivas-Cortez, Miguel, Bayrak, Gözde, Çınar, Tuğba, and Budak, Hüseyin
- Subjects
FRACTIONAL integrals ,CONVEX functions ,INTEGRAL inequalities ,DIFFERENTIABLE functions ,TRAPEZOIDS - Abstract
In this study, some new Hermite-Hadamard type inequalities for co-ordinated convex functions were obtained with the help of conformable fractional integrals. We have presented some remarks to give the relation between our results and earlier obtained results. Moreover, an identity for partial differentiable functions has been established. By using this equality and concept of co-ordinated convexity, we have proven a trapezoid type inequality for conformable fractional integrals. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
143. Quantum calculus with respect to another function.
- Author
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Nattapong Kamsrisuk, Donny Passary, Ntouyas, Sotiris K., and Jessada Tariboon
- Subjects
CALCULUS ,BOUNDARY value problems ,CALCULI ,INTEGRAL functions ,INTEGRAL inequalities - Abstract
In this paper, we studied the generalizations of quantum calculus on finite intervals. We presented the new definitions of the quantum derivative and quantum integral of a function with respect to another function and studied their basic properties. We gave an application of these newly defined quantum calculi by obtaining a new Hermite-Hadamard inequality for a convex function. Moreover, an impulsive boundary value problem involving quantum derivative, with respect to another function, was studied via the Banach contraction mapping principle. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
144. A new proof of a double inequality of Masjed-Jamei type.
- Author
-
Fen Wang
- Subjects
TANGENT function ,HYPERBOLIC functions ,SINE function ,INVERSE functions ,INTEGRAL inequalities - Abstract
In this paper, we provide a new simple proof of a double inequality of Masjed-Jamei type proved by L. Zhu. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
145. Reachable set estimation for neutral semi-Markovian jump systems with time-varying delay.
- Author
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Xipan Zhang, Changchun Shen, and Dingju Xu
- Subjects
MARKOVIAN jump linear systems ,TIME-varying systems ,INTEGRAL inequalities ,LINEAR matrix inequalities - Abstract
This work addresses the issue of finding ellipsoidal bounds of reachable sets for neutral semi-Markovian jump systems with time-varying delay and bounded peak disturbances, for which the related result has been rarely proposed for neutral semi-Markovian jump systems. Based on the modified improved Lyapunov-Krasovskii functional, a boundary of the reachable set for neutral semi-Markovian jump systems was obtained with the aid of utilizing a novel integral inequality and combining with the time-delay segmentation technique. The numerical examples are supplied to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
146. Lp gradient estimates and Calderón–Zygmund inequalities under Ricci lower bounds.
- Author
-
Marini, Ludovico, Meda, Stefano, Pigola, Stefano, and Veronelli, Giona
- Subjects
CURVATURE ,INTEGRALS ,GEOMETRY ,EQUATIONS ,INTEGRAL inequalities ,SENSES - Abstract
In this paper, we investigate the validity of first and second order L
p estimates for the solutions of the Poisson equation depending on the geometry of the underlying manifold. We first present Lp estimates of the gradient under the assumption that the Ricci tensor is lower bounded in a local integral sense, and construct the first counterexample showing that they are false, in general, without curvature restrictions. Next, we obtain Lp estimates for the second order Riesz transform (or, equivalently, the validity of Lp Calderón–Zygmund inequalities) on the whole scale 1 < p < ∞ by assuming that the injectivity radius is positive and that the Ricci tensor is either pointwise lower bounded, or non-negative in a global integral sense. When 1 < p ≤ 2, analogous Lp bounds on higher even order Riesz transforms are obtained provided that also the derivatives of Ricci are controlled up to a suitable order. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
147. On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator.
- Author
-
Tunç, Tuba and Demir, İzzettin
- Subjects
- *
FRACTIONAL calculus , *APPLIED mathematics , *APPLIED sciences , *FRACTIONAL integrals , *MATHEMATICS , *INTEGRAL inequalities - Abstract
In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
148. Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces.
- Author
-
Altwaijry, Najla, Dragomir, Silvestru Sever, and Feki, Kais
- Subjects
- *
HILBERT space , *POWER series , *INTEGRAL inequalities - Abstract
Consider the power series with complex coefficients h (z) = ∑ k = 0 ∞ a k z k and its modified version h a (z) = ∑ k = 0 ∞ | a k | z k . In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of h (z) on the open disk D (0 , ρ) , where ρ denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
149. Distributed State Estimation for Flapping-Wing Micro Air Vehicles with Information Fusion Correction.
- Author
-
Zhang, Xianglin, Luo, Mingqiang, Guo, Simeng, and Cui, Zhiyang
- Subjects
- *
MICRO air vehicles , *INTEGRAL inequalities , *TIME-varying networks , *DISTRIBUTED algorithms - Abstract
In this paper, we explore a nonlinear interactive network system comprising nodalized flapping-wing micro air vehicles (FMAVs) to address the distributed H ∞ state estimation problem associated with FMAVs. We enhance the model by introducing an information fusion function, leading to an information-fusionized estimator model. This model ensures both estimation accuracy and the completeness of FMAV topological information within a unified framework. To facilitate the analysis, each FMAV's received signal is individually sampled using independent and time-varying samplers. Transforming the received signals into equivalent bounded time-varying delays through the input delay method yields a more manageable and analyzable time-varying nonlinear network error system. Subsequently, we construct a Lyapunov–Krasovskii functional (LKF) and integrate it with the refined Wirtinger and relaxed integral inequalities to derive design conditions for the FMAVs' distributed H ∞ state estimator, minimizing conservatism. Finally, we validate the effectiveness and superiority of the designed estimator through simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
150. New Version of Fractional Pachpatte-Type Integral Inequalities via Coordinated ℏ-Convexity via Left and Right Order Relation.
- Author
-
Saeed, Tareq, Nwaeze, Eze R., Khan, Muhammad Bilal, and Hakami, Khalil Hadi
- Subjects
- *
INTEGRAL inequalities , *FRACTIONAL integrals , *INTEGRAL operators - Abstract
In particular, the fractional forms of Hermite–Hadamard inequalities for the newly defined class of convex mappings proposed that are known as coordinated left and right ℏ -convexity ( L R - ℏ -convexity) over interval-valued codomain. We exploit the use of double Riemann–Liouville fractional integral to derive the major results of the research. We also examine the key results' numerical validations that examples are nontrivial. By taking the product of two left and right coordinated ℏ -convexity, some new versions of fractional integral inequalities are also obtained. Moreover, some new and classical exceptional cases are also discussed by taking some restrictions on endpoint functions of interval-valued functions that can be seen as applications of these new outcomes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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