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This paper introduces and establishes new Hermite‐Hadamard type inequalities specifically tailored for m$$ m $$‐preinvex functions within the (p,q)$$ \left(p,q\right) $$‐calculus framework. These newly developed inequalities come with accompanying left‐right estimates, which enhance their practical utility. The primary objective of this research is to investigate the properties of (p,q)$$ \left(p,q\right) $$‐differentiable m$$ m $$‐preinvex functions and derive inequalities that extend and generalize existing results in the domain of integral inequalities. The techniques employed in this study hold broader implications, finding relevance in various fields where symmetry is paramount. The findings presented in this paper make a significant contribution to the field of analytic inequalities, offering valuable insights into the behavior and characteristics of m$$ m $$‐preinvex functions. Moreover, the established results demonstrate the wider applicability and generalization of analogous findings from prior literature. The techniques and inequalities introduced herein pave the way for further exploration and research in the realm of integral inequalities. [ABSTRACT FROM AUTHOR]

This paper mainly studies the synchronization problem of memristor-based bidirectional associative memory neural networks (MBAMNNs) via finite-time technology. Different from the existing neural network dynamic models, the given model in this paper is focused on the impact of parameter perturbation and strong mismatch, where strong mismatch includes parameter mismatch and time-varying delay mismatch. These characteristics can make the model be closer to the actual situation. A delay-independent feedback control scheme, which can stabilize the error system within finite-time regardless of whether the past state is known or not, is designed. It is worth noting that the constant is replaced by a function with the exponential term in the delay-independent controller, which can save the control cost to a certain extent. Based on the integral inequality technique, some sufficient conditions for MBAMNNs to converge to the equilibrium point within finite-time are provided. The validity and correctness of the theoretical results are finally confirmed by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order β approaches 1, in addition to the fractional integrals we examined. [ABSTRACT FROM AUTHOR]

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]

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]

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]

In this paper, we investigate the problem of stability of linear time-varying stochastic perturbed systems. We present sufficient conditions ensuring the global practical uniform exponential stability of a different class of stochastic perturbed systems based on generalized integral inequalities of Gronwall type. Finally, we provide numerical examples to prove the usefulness of the main results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present Katugampola fractional parameterized inequalities for s-convex function in the fourth sense. In the first place, with the help of integration by parts method, we provide a very important identity that will be of great significance for the next research. In addition, by comprehensively making use of some important concepts such as s-convex function in the fourth sense, Hölder’s integral inequality, and the well-known power-mean inequality, we establish three new parameterized inequalities. Finally, we provide some corollaries to help readers gain a deeper understanding of the theorems and the relevant theories. [ABSTRACT FROM AUTHOR]

The authors of the paper present a method to examine some Newton‐type inequalities for various function classes using Riemann‐Liouville fractional integrals. Namely, some fractional Newton‐type inequalities are established by using convex functions. In addition, several fractional Newton‐type inequalities are proved by using bounded functions by fractional integrals. Moreover, we construct some fractional Newton‐type inequalities for Lipschitzian functions. Furthermore, several Newton‐type inequalities are acquired by fractional integrals of bounded variation. Finally, we provide our results by using special cases of obtained theorems and examples. [ABSTRACT FROM AUTHOR]

Establishing a new integral inequality for the Riemann–Liouville fractional integral operator is the main objective of this paper. For twice differentiable s- (κ , H) -convex functions, we present a number of new inequalities that are connected to the Hermite–Hadamard integral inequality. [ABSTRACT FROM AUTHOR]

• Memory sampled-data control is applied for the uncertain rigid spacecraft model. • Randomly missing measurement in the system output obeys the Bernoulli distribution. • It tolerates uncertainty and disturbances using the H ∞ technique. • A novel looped and delay-dependent LKF is constructed for the proposed systems. • It gives the minimum disturbance attenuation level compared with existing works. This paper focuses on stabilizing the attitude of the rigid spacecraft under the sampled-data control design technique with constant communication delay. The system dynamics with model uncertainty (perturbation) and missing measurements are considered. The aim is to design a desirable attitude control that ensures the stabilization of the rigid spacecraft with an optimal H ∞ performance level. A novel Lyapunov–Krasovskii functional is developed, incorporating looped characteristics, for the proposed study on the rigid spacecraft model by developing relevant new terms. Making use of the Lyapunov function as well as free-matrix-based integral inequality, sufficient stability criteria are established to assure the stability of the rigid spacecraft model. Furthermore, the desired sampled-data control gain matrices are acquired through the solution of linear matrix inequalities, which guarantees the asymptotic stability of the rigid spacecraft model. Finally, the numerical simulation demonstrates the efficacy of the theoretical study proposed for the rigid spacecraft model. [ABSTRACT FROM AUTHOR]

This article explores integral inequalities within the framework of local fractional calculus, focusing on the class of generalized α$$ \alpha $$‐convex functions. It introduces a novel extension of the Hermite‐Hadamard inequality and derives numerous fractal inequalities through a novel multiparameterized identity. The primary aim is to generalize existing inequalities, highlighting that previously established results can be obtained by setting specific parameters within the main inequalities. The validity of the derived results is demonstrated through an illustrative example, accompanied by 2D and 3D graphical representations. Lastly, the paper discusses potential practical applications of these findings. [ABSTRACT FROM AUTHOR]

This paper employs two scalar parameters to extend auxiliary function-based integral inequality into a new formulations, say a parametrised auxiliary function-based integral inequality. Using these formulations, the constituent signals are utilised more efficiently by exploiting the interaction between them to reduce conservatism. Numerical example for stability analysis of linear systems with time-varying delay shows the improved performance of the proposed new formulations in terms of maximum delay bounds and decision variables. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying some new reverse Hölder-type inequalities associated with the dynamic integral called diamond on time scale, which is expressed as an ’approximate’ symmetric integral on time scales. Some related inequalities are also presented. The obtained inequalities extend known results related with discrete and continuous forms. [ABSTRACT FROM AUTHOR]

Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ -pre-invex interval-valued mappings ( C · L · R - ℏ -pre-invex Ι · V - M ), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte's type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes. [ABSTRACT FROM AUTHOR]

Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann's integral theory, the Hermite–Hadamard's type inequalities are introduced for a newly defined class of nonconvex functions, which is known as  U · D preinvex fuzzy number-valued mappings ( U · D preinvex  F · N · V · M s) on coordinates. Some Pachpatte-type inequalities are also established for the product of two  U · D preinvex  F · N · V · M s, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann's integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made. [ABSTRACT FROM AUTHOR]

The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings ( F - N - V - M s ), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard ( H ⋅ H ) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes. [ABSTRACT FROM AUTHOR]

In this paper, the μ-state estimation issue for Markovian switching complex-valued neural networks with mixed delays has been addressed. To conserve communication resources, an effective event-triggered mechanism is proposed, which relays on a Markovian switching positive threshold. By resorting to Lyapunov stability theory, stochastic analysis method and matrix inequalities technique, some sufficient criteria are established to guarantee the estimation error system is stochastic μ-stable in the mean sense. Moreover, the expected estimator gain matrices can be accurately achieved by solving some obtained matrix inequalities. Besides, it is should be pointed that the μ-stability involves exponential, power, and logarithmic stability, which expands a mass of existed relevant results. In the end, for power stability, one numerical example is provided to substantiate the effectiveness and credibility of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper concentrates on addressing fractional inequalities for exponential type convex functions. By means of exponential-type convexity, we firstly establish Hermite-Hadamard (HH) type inequalities for fractional integrals with exponential kernels. Secondly, based on the discovered fractional identity by separating [a; b] to n equal subintervals, and the fact that the twice derivative in absolute value is exponential type convex, we present multipoint-based HH inequalities, which cover the trapezoid- and Bullen-type inequalities for n = 1 and 2, correspondingly. During the period, some numerical examples with graphs are provided to show the validity of the deduced inequalities. [ABSTRACT FROM AUTHOR]

Integral inequalities are very useful in finding the error bounds for numerical integration formulas. In this paper, we prove some multiplicative integral inequalities for first-time differentiable s-convex functions. These new inequalities help in finding the error bounds for different numerical integration formulas in multiplicative calculus. The use of s-convex function extends the results for convex functions and covers a large class of functions, which is the main motivation for using s-convexity. To prove the inequalities, we derive two different integral identities for multiplicative differentiable functions in the setting of multiplicative calculus. Then, with the help of these integral identities, we prove some integral inequalities of the Simpson and Ostrowski types for multiplicative generalized convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities, to show the validity of the results for multiplicative s-convex functions. We also give some applications to quadrature formula and special means of real numbers within the framework of multiplicative calculus. [ABSTRACT FROM AUTHOR]

Unfortunately, eleven of our provinces were severely affected due to two severe earthquakes that occurred in our country, the Republic of Turkey, on February 6, 2023. As a result, thousands of buildings were destroyed and tens of thousands of our citizens lost their lives. From past to present, such disasters have occurred in many parts of our world and will continue to happen. In order to raise awareness for researchers and academicians reading our article, we will give a new definition of convexity in this article, and we will call it "earthquake convexity". In this paper, we study some algebraic properties of the earthquake convexity. Then we compare the results obtained with both Hölder, Hölder–İşcan inequalities and power-mean, improved power-mean integral inequalities and show that the results obtained with Hölder–İşcan and improved power-mean inequalities are better than the others. Some applications to special means of real numbers are also given. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [ABSTRACT FROM AUTHOR]

In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann–Liouville fractional integrals and Riemann integrals. [ABSTRACT FROM AUTHOR]

In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error bounds for Simpson's second formula, namely Newton–Cotes quadrature formula for differentiable convex functions in the framework of tempered fractional integrals and classical calculus. Furthermore, it is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. [ABSTRACT FROM AUTHOR]

In this paper, by using the Riccati transformation and integral inequality technique, we establish several oscillation criteria for second-order Emden–Fowler neutral delay differential equations under the canonical case and non-canonical case, respectively. Compared with some recent results reported in the literature, we extend the range of the neutral coefficient. Therefore, our results generalize to some of the results presented in the literature. Furthermore, several examples are provided to illustrate our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain several results on the global existence, uniqueness and attractivity for fractional evolution equations involving the Riemann-Liouville type by exploiting some results on weakly singular integral inequalities in Banach spaces. Some boundedness conditions of the nonlinear term are considered to obtain the main results that generalize and improve some well-known works. [ABSTRACT FROM AUTHOR]

In this paper, the tempered Ψ –Riemann–Liouville fractional derivative and the tempered Ψ –Caputo fractional derivative of order n − 1 < α < n ∈ N are introduced for C n − 1 –functions. A nonlinear version of the second Henry–Gronwall inequality for integral inequalities with the tempered Ψ –Hilfer fractional integral is derived. By using this inequality, an existence and uniqueness result and a sufficient condition for the non-existence of blow-up solutions of nonlinear tempered Ψ –Caputo fractional differential equations are proved. Illustrative examples are given. [ABSTRACT FROM AUTHOR]

In the present paper, utilizing a wide class of fractional integral operators (namely the Raina fractional operator), we develop novel fractional integral inequalities of the Hermite–Hadamard type. With the help of the well-known Riemann–Liouville fractional operators, s-type convex functions are derived using the important results. We also note that some of the conclusions of this study are more reasonable than those found under certain specific conditions, e.g., s = 1 , λ = α ,   σ (0) = 1 , and w = 0 . In conclusion, the methodology described in this article is expected to stimulate further research in this area. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of complex-valued neural networks (CVNNs) with semi-Markovian jump (sMJ) and generally uncertain transition rates. Each transition rate may be totally unknown or its estimate is determined. Firstly, two improved reciprocally convex inequalities (RCIs) and three less conservative integral inequalities are generalized to the complex-valued domain. Secondly, the existence and uniqueness of the addressed networks are proposed by the complex-valued homeomorphism theorem. Thirdly, by constructing a Lyapunov–Krasovskii functional (LKF), delay-dependent robust stability criteria of the CVNNs are obtained by utilizing the improved complex-valued RCIs and integral inequalities. Finally, simulations are presented to demonstrate the effectivenes and practicality of the established method. [ABSTRACT FROM AUTHOR]

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]

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger's inequality for the integral terms instead of the traditional and more conservative Jensen's condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates. [ABSTRACT FROM AUTHOR]

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]

In this paper, a new integral identity is provided. Based on this equality, Simpson-type dual integral inequalities for functions whose first derivatives are s-convex via Riemann–Liouville fractional integrals are established. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

In this paper, we investigate the validity of first and second order Lp 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]

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]

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]

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]

This paper is concerned with the finite-time annular domain stability and stabilisation for the positive systems. A new analysis method is proposed to obtain less conservative finite-time annular domain stability criteria and its superiority to modified Gronwall inequality is analysed. Moreover, conditions for the existence of state feedback and observer-based controllers that guarantee the closed-loop system to be positive and finite-time annular domain stable are given under the linear programming framework. Finally, two numerical examples are provided to show the effectiveness and superiority of the theoretical results. [ABSTRACT FROM AUTHOR]

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]

This paper introduces novel generalizations of dynamic inequalities of Copson type within the framework of time scales delta calculus. The proposed generalizations leverage mathematical tools such as Hölder's inequality, Minkowski's inequality, the chain rule on time scales, and the properties of power rules on time scales. As special cases of our results, particularly when the time scale T equals the real line ( T = R ), we derive some classical continuous analogs of previous inequalities. Furthermore, when T corresponds to the set of natural numbers including zero ( T = N 0 ), the obtained results, to the best of the authors' knowledge, represent innovative contributions to the field. [ABSTRACT FROM AUTHOR]

In this paper, by using both the Hölder, power‐mean integral inequalities and Hölder‐İşcan, improved power‐mean integral inequalities that give approach better than Hölder and power‐mean inequalities respectively, some new Ostrowski type inequalities are derived for multiplicatively P‐function. The results obtained in both cases are compared and the results obtained using Hölder‐İşcan and improved power‐mean integral inequalities are proven to be better. Some applications to special means of real numbers are given. [ABSTRACT FROM AUTHOR]

This paper is consecrated to the asymptotic behavior of a coupled system consisting of the Kirchhoff and heat equations in a bounded domain. We establish that the problem is well-posed by using a Faedo–Galerkin scheme. Furthermore, the energy method combined with the multiplier techniques is used to show the exponential stability of the solutions to the system. [ABSTRACT FROM AUTHOR]

In this paper we introduce necessary and sufficient conditions for a real-valued function to be preinvex. Some properties of preinvex functions and new versions of Jensen's integral type inequality in this setting are given. Several examples are also involved. [ABSTRACT FROM AUTHOR]