7,603 results
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2. Weighted Milne-type inequalities through Riemann-Liouville fractional integrals and diverse function classes.
- Author
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Almoneef, Areej A., Hyder, Abd-Allah, and Budak, Hüseyin
- Subjects
FRACTIONAL integrals ,INTEGRAL functions ,FUNCTIONS of bounded variation ,CONVEX functions ,DIFFERENTIABLE functions ,ANALYTIC functions - Abstract
This research paper investigated weighted Milne-type inequalities utilizing Riemann-Liouville fractional integrals across diverse function classes. A key contribution lies in the establishment of a fundamental integral equality, facilitated by the use of a nonnegative weighted function, which is pivotal for deriving the main results. The paper systematically proved weighted Milne-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. The obtained results not only contribute to the understanding of Milne-type inequalities but also offer insights that pave the way for potential future research in the considered topics. Furthermore, it is evident that the results obtained encompass numerous findings that were previously presented in various studies as special cases. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. A METHOD FOR PROVING REFINEMENTS OF INEQUALITIES RELATED TO CONVEX FUNCTIONS ON INTERVALS.
- Author
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HORVÁTH, LÁSZLÓ
- Subjects
JENSEN'S inequality ,INTEGRAL inequalities - Abstract
In this paper, using the results of a recent paper by the author, we give a new method for proving refinements of inequalities related to convex functions on intervals. In many cases, the proof is simpler and more transparent than using the usual techniques, and the essence of the refinement is clearer. This is illustrated by two refinements of the Jensen’s inequality and one refinement of the Lah-Ribarič inequality. As an application we generalize a recent result for strongly convex functions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. Simpson type Tensorial Inequalities for Continuous functions of Selfadjoint operators in Hilbert Spaces.
- Author
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Stojiljković, V.
- Subjects
SELFADJOINT operators ,HILBERT space ,CONTINUOUS functions ,OPERATOR functions ,CONVEX functions - Abstract
In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities are obtained with variations due to the convexity properties of the mapping f || 1/6 [f(A) x 1 + 4f - A - 1 + 1 B 2 - + 1 f(B) - - Z 1 0 f((1 - k)A < 1 + k1 B)dk || 5\36 1 B-A 1 f'I,+8. [ABSTRACT FROM AUTHOR]
- Published
- 2024
5. INEQUALITIES FOR FUNCTIONS CONVEX ON THE COORDINATES WITH APPLICATIONS TO JENSEN AND HERMITE--HADAMARD TYPE INEQUALITIES, AND TO NEW DIVERGENCE FUNCTIONALS.
- Author
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HORVATH, LASZLO
- Subjects
CONVEX functions ,MATHEMATICAL inequalities ,HADAMARD matrices ,COORDINATES ,JENSEN'S inequality - Abstract
In this paper we show that inequalities for functions convex on the coordinates can be derived from inequalities for convex functions defined on real intervals, and essentially only this method works. As applications, we show how our result works for the Jensen's and Hermite- Hadamard inequalities for functions convex on the coordinates. Finally, we extend the classical notion of f -divergence functional to functions convex on the coordinates, and as a further application of our main result, we study the refinement of a basic inequality corresponding to the new divergence. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. On Approximate Variational Inequalities and Bilevel Programming Problems.
- Author
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Upadhyay, Balendu Bhooshan, Stancu-Minasian, Ioan, Poddar, Subham, and Mishra, Priyanka
- Subjects
BILEVEL programming ,SUBDIFFERENTIALS ,CONVEX functions - Abstract
In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local ϵ -quasi solutions of the BLPP, under generalized approximate convexity assumptions, via limiting subdifferentials. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (KKM)-Fan's lemma, we derive some existence results for the solutions of AMTVI and ASTVI. We have furnished suitable, non-trivial, illustrative examples to demonstrate the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that explores relationships between the approximate variational inequalities and BLPP under the assumptions of generalized approximate convexity by employing the powerful tool of limiting subdifferentials. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels.
- Author
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Li, Hong, Meftah, Badreddine, Saleh, Wedad, Xu, Hongyan, Kiliçman, Adem, and Lakhdari, Abdelghani
- Subjects
CONVEX functions ,DIFFERENTIABLE functions ,INTEGRAL inequalities ,INTEGRAL operators ,INTEGRALS - Abstract
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]
- Published
- 2024
- Full Text
- View/download PDF
8. A Two-Layer Recurrent Neural Network for Nonsmooth Convex Optimization Problems.
- Author
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Qin, Sitian and Xue, Xiaoping
- Subjects
- *
NEURAL circuitry , *PHOTOGRAPHIC paper , *CONVEX functions , *PHOTOGRAPHIC printing , *HOROLOGY , *LINEAR programming - Abstract
In this paper, a two-layer recurrent neural network is proposed to solve the nonsmooth convex optimization problem subject to convex inequality and linear equality constraints. Compared with existing neural network models, the proposed neural network has a low model complexity and avoids penalty parameters. It is proved that from any initial point, the state of the proposed neural network reaches the equality feasible region in finite time and stays there thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region. The equilibrium point set of the proposed neural network is proved to be equivalent to the Karush–Kuhn–Tucker optimality set of the original optimization problem. It is further proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov. Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of the proposed neural network. Finally, as applications, the proposed neural network is used to solve nonlinear convex programming with linear constraints and L1 -norm minimization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
9. Asynchronously switching control of discrete-time switched systems with a Φ-dependent integrated dwell time approach.
- Author
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Qiang Yu and Na Xue
- Subjects
DISCRETE-time systems ,LINEAR matrix inequalities ,LYAPUNOV functions ,EXPONENTIAL stability ,CONVEX functions - Abstract
In this paper, the asynchronous control problem is investigated and a multiple convex Lyapunov functions (MCLF) approach is introduced for a class of discrete-time switched linear systems under the Φ-dependent integrated dwell time (ΦDIDT) switching strategy. For the problem of asynchronous switching, this paper considers that Lyapunov functions may jump when the subsystem switches or the controller changes. Thus, the constructed MCLF is dependent on both the asynchronous interval and the synchronous interval, and the synchronous interval is divided into the convex interval and non-convex interval parts. Some sufficient conditions of stability with Linear matrix inequality (LMI) forms are obtained, and the asynchronous controller is designed to guarantee the globally uniform exponential stability of the system under study. In addition, the proposed method can degenerate to the existing methods to deal with the asynchronous control problem. Finally, a numerical example illustrates the superiority of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
10. TWICE DIFFERENTIABLE OSTROWSKI TYPE TENSORIAL NORM INEQUALITY FOR CONTINUOUS FUNCTIONS OF SELFADJOINT OPERATORS IN HILBERT SPACES.
- Author
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STOJILJKOVIĆ, V.
- Subjects
SELFADJOINT operators ,HILBERT space ,CONTINUOUS functions ,OPERATOR functions ,CONVEX functions - Abstract
In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert space have been obtained. The recent progression of the Hilbert space inequalities following the definition of the convex operator inequality has lead researchers to explore the concept of Hilbert space inequalities even further. The motivation for this paper stems from the recent development in the theory of tensorial and Hilbert space inequalities. Multiple inequalities are obtained with variations due to the convexity properties of the mapping f... 1 6 A01 + 10 B 2) -exp(A) 0 1 + 4 exp +10exp(B) 1-4 + ∣ exp((--~-a 0 1 1 C + k} 1 0 b) k-1 dk ∕ exp-1 -- A 0 1 + k 1 0 (1 -- k)- 2dk-|| 47 ≤ "1 0 B -- A 0 1∣∣2 (Hexp(A)H + l∣exp(B)∣∣)∙ 360 Tensorial version of a Lemma given by Hezenci is derived and utilized to obtain the desired inequalities. in the introduction section is given a brief history of the inequalities, while in the preliminary section we give necessary Lemmas and results in order to understand the paper. Structure and novelty of the paper are discussed at the end of the introduction section. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
11. Inclusion and Neighborhood on a Multivalent q-Symmetric Function with Poisson Distribution Operators.
- Author
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Amini, Ebrahim, Al-Omari, Shrideh, and Suthar, Dayalal
- Subjects
SYMMETRIC functions ,POISSON distribution ,STAR-like functions ,CONVEX functions ,STOCHASTIC convergence - Abstract
In this paper, by using Poisson distribution probability, some characteristics of analytic multivalent q -symmetric starlike and q -symmetric convex functions of order η are examined. Then, by utilizing the Poisson distribution and the concept of the q -analogue Salagean integral operator, the p -valent convergence polynomial was introduced. Furthermore, a number of subclasses of analytic symmetric p -valent functions linked to novel polynomials are also deduced. After that, specific coefficient constraints are determined and symmetric δ , q -neighborhoods for p -valent functions are defined. In relation to symmetric δ , q -neighborhoods of q -symmetric p -valent functions formed by Poisson distributions, this paper presents new inclusion results. In addition, a detailed discussion of certain q -symmetric inequalities of analytic functions with negative coefficients is also provided. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
12. Analytical and geometrical approach to the generalized Bessel function.
- Author
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Bulboacă, Teodor and Zayed, Hanaa M.
- Subjects
INTEGRAL transforms ,BESSEL functions ,CONVEX functions ,MATHEMATICAL notation - Abstract
In continuation of Zayed and Bulboacă work in (J. Inequal. Appl. 2022:158, 2022), this paper discusses the geometric characterization of the normalized form of the generalized Bessel function defined by V ρ , r (z) : = z + ∑ k = 1 ∞ (− r) k 4 k (1) k (ρ) k z k + 1 , z ∈ U , for ρ , r ∈ C ∗ : = C ∖ { 0 } . Precisely, we will use a sharp estimate for the Pochhammer symbol, that is, Γ (a + n) / Γ (a + 1) > (a + α) n − 1 , or equivalently (a) n > a (a + α) n − 1 , that was firstly proved by Baricz and Ponnusamy for n ∈ N ∖ { 1 , 2 } , a > 0 and α ∈ [ 0 , 1.302775637 ... ] in (Integral Transforms Spec. Funct. 21(9):641–653, 2010), and then proved in our paper by another method to improve it using the partial derivatives and the two-variable functions' extremum technique for n ∈ N ∖ { 1 , 2 } , a > 0 and 0 ≤ α ≤ 2 , and used to investigate the orders of starlikeness and convexity. We provide the reader with some examples to illustrate the efficiency of our theory. Our results improve, complement, and generalize some well-known (nonsharp) estimates, as seen in the Concluding Remarks and Outlook section. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
13. Open issues and recent advances in DC programming and DCA.
- Author
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Le Thi, Hoai An and Pham Dinh, Tao
- Subjects
APPLIED sciences ,NONCONVEX programming ,GLOBAL optimization ,NONSMOOTH optimization ,CONVEX functions ,RESEARCH personnel - Abstract
DC (difference of convex functions) programming and DC algorithm (DCA) are powerful tools for nonsmooth nonconvex optimization. This field was created in 1985 by Pham Dinh Tao in its preliminary state, then the intensive research of the authors of this paper has led to decisive developments since 1993, and has now become classic and increasingly popular worldwide. For 35 years from their birthday, these theoretical and algorithmic tools have been greatly enriched, thanks to a lot of their applications, by researchers and practitioners in the world, to model and solve nonconvex programs from many fields of applied sciences. This paper is devoted to key open issues, recent advances and trends in the development of these tools to meet the growing need for nonconvex programming and global optimization. We first give an outline in foundations of DC programming and DCA which permits us to highlight the philosophy of these tools, discuss key issues, formulate open problems, and bring relevant answers. After outlining key open issues that require deeper and more appropriate investigations, we will present recent advances and ongoing works in these issues. They turn around novel solution techniques in order to improve DCA's efficiency and scalability, a new generation of algorithms beyond the standard framework of DC programming and DCA for large-dimensional DC programs and DC learning with Big data, as well as for broader classes of nonconvex problems beyond DC programs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. Convex Regularized Recursive Minimum Error Entropy Algorithm.
- Author
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Wang, Xinyu, Ou, Shifeng, and Gao, Ying
- Subjects
COST functions ,BURST noise ,ALGORITHMS ,CONVEX functions - Abstract
It is well known that the recursive least squares (RLS) algorithm is renowned for its rapid convergence and excellent tracking capability. However, its performance is significantly compromised when the system is sparse or when the input signals are contaminated by impulse noise. Therefore, in this paper, the minimum error entropy (MEE) criterion is introduced into the cost function of the RLS algorithm in this paper, with the aim of counteracting the interference from impulse noise. To address the sparse characteristics of the system, we employ a universally applicable convex function to regularize the cost function. The resulting new algorithm is named the convex regularization recursive minimum error entropy (CR-RMEE) algorithm. Simulation results indicate that the performance of the CR-RMEE algorithm surpasses that of other similar algorithms, and the new algorithm excels not only in scenarios with sparse systems but also demonstrates strong robustness against pulse noise. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. NEW ITERATIVE SCHEMES FOR GENERAL HARMONIC VARIATIONAL INEQUALITIES.
- Author
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NOOR, MUHAMMAD ASLAM and NOOR, KHALIDA INAYAT
- Subjects
CONVEX sets ,HARMONIC functions ,VARIATIONAL inequalities (Mathematics) ,CONVEX functions ,SET functions - Abstract
Some new classes of general harmonic convex sets and convex functions are introduced and studied in this paper. The optimality criteria of the differentiable general harmonic functions is characterized by the general harmonic variational inequalities. Special cases are also pointed out as applications of the new concepts. Auxiliary principle technique involving an arbitrary operator is applied to suggest and analysis several inertial type methods are suggested. Convergence criteria is investigated of the proposed methods under weaker conditions. The results obtained in this paper may inspire further research along with implementable numerical methods for solving the general harmonic variational inequalities and related optimization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. BOUNDS FOR THE α-ADJACENCY ENERGY OF A GRAPH.
- Author
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SHABAN, REZWAN UL, IMRAN, MUHAMMAD, and GANIE, HILAL A.
- Subjects
GRAPH theory ,EIGENVALUES ,CONVEX functions ,RAYLEIGH quotient ,GRAPH connectivity - Abstract
For the adjacency matrix A(G) and diagonal matrix of the vertex degrees D(G) of a simple graph G, the A(G) matrix is the convex combinations of D(G) and A(G), and is defined as A(G) = D(G)+(1)A(G), for 0 n be the eigenvalues of A(G) (which we call -adjacency eigenvalues of the graph G). The generalized adjacency energy also called -adjacency energy of the graph G is defined as EA (G) = is the average vertex degree, m is the size and n is the order of G. The -adjacency energy of a graph G merges the theory of energy (adjacency energy) and the signless Laplacian energy, as EA0 (G) = E (G) and 2E A 12 (G) = QE(G), where E (G) is the energy and QE(G) is the signless Laplacian energy of G. In this paper, we obtain some new upper and lower bounds for the generalized adjacency energy of a graph, in terms of different graph parameters like the vertex covering number, the Zagreb index, the number of edges, the number of vertices, etc. We characterize the extremal graphs attained these bounds. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. Some remarks on parameterized inequalities involving conformable fractional operators.
- Author
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ÜNAL, Cihan, HEZENCI, Fatih, and BUDAK, Hüseyin
- Subjects
CONVEX functions ,FRACTIONAL integrals ,DIFFERENTIABLE functions ,FRACTIONAL calculus - Abstract
In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
18. New Developments in Geometric Function Theory.
- Author
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Oros, Georgia Irina
- Subjects
GEOMETRIC function theory ,UNIVALENT functions ,ANALYTIC functions ,MEROMORPHIC functions ,CONVEX functions ,FRACTIONAL calculus - Abstract
A previously introduced operator defined by applying the Riemann-Liouville fractional integral to the convex combination of well-known Ruscheweyh and Salagean differential operators is used for defining a new fuzzy subclass. The authors suggest that the operator introduced here can be utilized to define other classes of analytic functions or to generalize other types of differential operators. The new operator defined in this paper can be used to introduce other specific subclasses of analytic functions, and quantum calculus can be also investigated in future studies. The fractional differential operator and the Mittag-Leffler functions are combined to formulate and arrange a new operator of fractional calculus. [Extracted from the article]
- Published
- 2023
- Full Text
- View/download PDF
19. Subclasses of convex functions on the unit disc of the complex plane
- Author
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Aron, Mihai
- Published
- 2024
- Full Text
- View/download PDF
20. Generalized strongly n-polynomial convex functions and related inequalities.
- Author
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Özcan, Serap, Kadakal, Mahir, İşcan, İmdat, and Kadakal, Huriye
- Subjects
INTEGRAL inequalities ,CONVEX functions ,LITERATURE - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Operator upper bounds for Davis-Choi-Jensen's difference in Hilbert spaces.
- Author
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DRAGOMIR, SILVESTRU SEVER
- Subjects
OPERATOR functions ,JENSEN'S inequality ,CONVEX functions ,LINEAR operators - Abstract
In this paper we obtain several operator inequalities providing upper bounds for the Davis-Choi-Jensen's Difference Φ(f (A)) -- f (Φ (A)) for any convex function f : I → R, any selfadjoint operator A in H with the spectrum Sp (A) ⊂ I and any linear, positive and normalized map Φ : B (H) → B (K), where H and K are Hilbert spaces. Some examples of convex and operator convex functions are also provided. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. THE SHARP BOUNDS OF THE HANKEL DETERMINANTS FOR THE CLASS OF CONVEX FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS.
- Author
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RATH, BISWAJIT, KUMAR, K. SANJAY, KRISHNA, D. VAMSHEE, and VISWANADH, G. K. SURYA
- Subjects
SYMMETRIC functions ,CONVEX functions ,HANKEL functions ,ANALYTIC functions ,DETERMINANTS (Mathematics) - Abstract
In this paper, we estimate sharp bounds for certain Hankel determinants, H
2,3 (f), H3,1 (f) and Zalcman functional |a²3 -- a5 | for the class of convex function with respect to symmetric points, hence proving the recent conjecture made by Virendra et al., that affirms the sharp bound for the third Hankel determinant in the classes of convex functions with respect to symmetric points is 4/135. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
23. Simpson Type Tensorial Norm Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces.
- Author
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STOJILJKOVIĆ, VUK
- Subjects
SELFADJOINT operators ,CONTINUOUS functions ,OPERATOR functions ,CONVEX functions - Abstract
In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities of the form.. are obtained with variations due to the convexity properties of the mapping f. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Variations in the Tensorial Trapezoid Type Inequalities for Convex Functions of Self-Adjoint Operators in Hilbert Spaces.
- Author
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Stojiljković, Vuk, Mirkov, Nikola, and Radenović, Stojan
- Subjects
HILBERT space ,CONVEX functions ,OPERATOR functions ,TRAPEZOIDS ,SELFADJOINT operators ,CONTINUOUS functions - Abstract
In this paper, various tensorial inequalities of trapezoid type were obtained. Identity from classical analysis is utilized to obtain the tensorial version of the said identity which in turn allowed us to obtain tensorial inequalities in Hilbert space. The continuous functions of self-adjoint operators in Hilbert spaces have several tensorial norm inequalities discovered in this study. The convexity features of the mapping f lead to the variation in several inequalities of the trapezoid type. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Zero-Norm ELM with Non-convex Quadratic Loss Function for Sparse and Robust Regression.
- Author
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Wang, Xiaoxue, Wang, Kuaini, She, Yanhong, and Cao, Jinde
- Subjects
MACHINE learning ,CONVEX functions - Abstract
Extreme learning machine (ELM) is a machine learning technique with simple structure, fast learning speed, and excellent generalization ability, which has received a lot of attention since it was proposed. In order to further improve the sparsity of output weights and the robustness of the model, this paper proposes a sparse and robust ELM based on zero-norm regularization and a non-convex quadratic loss function. The zero-norm regularization obtains sparse hidden nodes automatically, and the introduced non-convex quadratic loss function enhances the robustness by setting constant penalties to outliers. The optimization problem can be formulated as the difference of convex functions (DC) programming. This DC programming is solved by using the DC algorithm (DCA) in this paper. The experiments on the artificial and Benchmark datasets verify that the proposed method has promising robustness while reducing the number of hidden nodes, especially on the datasets with higher outliers level. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. HERMITE--HADAMARD INTEGRAL INEQUALITY FOR HARMONICALLY CONVEX FUNCTIONS VIA RIEMANN--LIOUVILLE FRACTIONAL INTEGRALS.
- Author
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TIWARI, PITAMBER and BHATTA, CHET RAJ
- Subjects
INTEGRAL inequalities ,MATHEMATICAL inequalities ,MATHEMATICS theorems ,CONVEX functions ,PROBABILITY theory - Abstract
The concept of convexity of functions is a useful instrument that is used to solve a wide range of pure and applied scientific issues. The Hermite-Hadamard inequality which is also used frequently in many other parts of practical mathematics notably in optimization and probability is one of the most important mathematical inequalities relevant to convex maps. The fractional calculus, a calculus of non-integer order has applications in diverse fields of physical sciences. In this paper, we have established Hermite-Hadamard's inequalities via Riemann-Liouville fractional integral for the case of harmonically convex function as well as the products of two harmonically convex functions via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
27. Approximate Convexity for Set-Valued Maps.
- Author
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Kefayati, Zohreh and Oveisiha, Morteza
- Subjects
SET-valued maps ,APPROXIMATION theory ,SUBDIFFERENTIALS ,MONOTONIC functions ,CONVEX functions - Abstract
In this paper, we extend the notion of approximate convexity to setvalued maps and obtain some relations between approximate convexity and approximate monotonicity of their normal subdifferential. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
28. Adaptive Variant of the Frank–Wolfe Algorithm for Convex Optimization Problems.
- Author
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Aivazian, G. V., Stonyakin, F. S., Pasechnyk, D. A., Alkousa, M. S., Raigorodsky, A. M., and Baran, I. V.
- Subjects
SMOOTHNESS of functions ,CONVEX sets ,CONVEX functions ,MULTIPLICATION ,SOCIAL dominance - Abstract
In this paper, we investigate a variant of the Frank–Wolfe method for convex optimization problems with the adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient). Theoretical estimates of the quality of the approximate solution provided by the method using adaptively selected parameters L
k are presented. For a class of problems on a convex feasible set with a convex objective function, the guaranteed convergence rate of the proposed method is sublinear. A special subclass of these problems (an objective function with the gradient dominance condition) is considered and the convergence rate of the method using adaptively selected parameters Lk is estimated. An important feature of the result obtained is the elaboration of the case where it is possible to guarantee, after the completion of the iteration, at least double reduction in the residual of the function. At the same time, the use of adaptively selected parameters in theoretical estimates makes the method applicable to both smooth and non-smooth problems, provided that the iteration termination criterion is met. For smooth problems, it can be proved that the theoretical estimates of the method are reliably optimal up to multiplication by a constant factor. Computational experiments are carried out and a comparison with two other algorithms is made to demonstrate the efficiency of the algorithm on a number of both smooth and non-smooth problems. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
29. Extension of Milne-type inequalities to Katugampola fractional integrals.
- Author
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Lakhdari, Abdelghani, Budak, Hüseyin, Awan, Muhammad Uzair, and Meftah, Badreddine
- Abstract
This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Sharp Coefficient Results on the Inverse of Silverman Starlike Functions.
- Author
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Shi, L. and Arif, M.
- Abstract
In the present paper, we consider a subclass of starlike functions introduced by Silverman. It is defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the sharp bounds of coefficient problems for the inverse of functions in this class. We derive the upper bounds of some initial coefficients, the Fekete–Szegö type inequality and the second Hankel determinant for . On the third Hankel determinant , we give a bound on the inverse of . All the results are proved to be sharp. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. A collective neurodynamic approach to distributed resource allocation with event-triggered communication.
- Author
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Cai, Xin, Gao, Bingpeng, and Nan, Xinyuan
- Subjects
CONSTRAINED optimization ,RESOURCE allocation ,RECURRENT neural networks ,CONVEX sets ,GLOBAL optimization ,CONVEX functions - Abstract
To solve a distributed optimal resource allocation problem, a collective neurodynamic approach based on recurrent neural networks (RNNs) is proposed in this paper. Multiple RNNs cooperatively solve a global constrained optimization problem in which the objective function is a total of local non-smooth convex functions and is subject to local convex sets and a global equality constraint. Different from the projection dynamics to deal with local convex sets in the existing work, an internal dynamics with projection output is designed in the algorithm to relax the Slater's condition satisfied by the optimal solution. To overcome continuous-time communication in a group of RNNs, an aperiodic communication scheme, called the event-triggered scheme, is presented to alleviate communication burden. It is analyzed that the convergence of the designed collective neurodynamic approach based on the event-triggered communication does not rely on global information. Furthermore, it is proved the freeness of the Zeno behavior in the event-triggered scheme. Two examples are presented to illustrate the obtained results [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Constrained minimum variance and covariance steering based on affine disturbance feedback control parameterization.
- Author
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Balci, Isin M. and Bakolas, Efstathios
- Subjects
- *
STOCHASTIC control theory , *MINIMUM variance estimation , *COVARIANCE matrices , *UNCERTAIN systems , *CONVEX functions , *PARAMETERIZATION , *LINEAR matrix inequalities - Abstract
This paper deals with finite‐horizon minimum‐variance and covariance steering problems subject to constraints. The goal of the minimum variance problem is to steer the state mean of an uncertain system to a prescribed vector while minimizing the trace of its terminal state covariance whereas the goal in the covariance steering problem is to steer the covariance matrix of the terminal state to a prescribed positive definite matrix. The paper proposes a solution approach that relies on a stochastic version of the affine disturbance feedback control parametrization. In this control policy parametrization, the control input at each stage is expressed as an affine function of the history of disturbances that have acted upon the system. It is shown that this particular parametrization reduces the stochastic optimal control problems considered in this paper into tractable convex programs or difference of convex functions programs with essentially the same decision variables. In addition, the paper proposes a variation of this control parametrization that relies on truncated histories of past disturbances, which allows for sub‐optimal controllers to be designed that strike a balance between performance and computational cost. The suboptimality of the truncated policies is formally analyzed and closed form expressions are provided for the performance loss due to the use of the truncation scheme. Finally, the paper concludes with a comparative analysis of the truncated versions of the proposed policy parametrization and other standard policy parametrizations through numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Insight into the gas–liquid transition from the Berthelot model.
- Author
-
Mi, Li-Qin, Li, Dandan, Li, Shanshan, and Li, Zhong-Heng
- Subjects
- *
THERMODYNAMICS , *FIRST-order phase transitions , *EQUATIONS of state , *PHASE transitions , *CONVEX functions , *LATENT heat - Abstract
We extend the parametric method developed for the van der Waals model by Lekner [Am. J. Phys. 50(2), 161–163 (1982)] to other equations of state, particularly the Berthelot model, thereby making the testing of these equations of state much faster and simpler. We systematically investigate important properties of first-order phase transitions in the Berthelot model. Thermodynamic properties near the critical point are discussed and the predictions of the Berthelot and van der Waals models are compared with experimental data. The Berthelot equation affords an improved fit to the density–temperature coexistence curve for many substances when compared to the van der Waals equation. A failure of the Berthelot model is its prediction of latent heat and heat capacities that are convex functions at lower temperatures. We also examine two modifications of the Berthelot equation of state that, like the van der Waals model, are also solvable by the parameter method. These, which we call the cPF and dPF models, reduce to the van der Waals and Berthelot models in different limits of their parameters. They give improved fits to the experimental data away from the critical point but involve an additional fitting parameter. Editor's note: While the van der Waals equation of state provides a simple model for phase transitions, it fails to achieve a good quantitative fit for properties near phase transitions in most substances. A closely related model, the Berthelot model, still has only two free parameters, but it allows the attraction between molecules to depend not only on volume but also on temperature. This paper builds on the parametric expressions for the van der Waals gas derived in a 1982 paper in this journal by John Lekner. It shows that similar expressions derived from the Berthelot model provide a much better fit to the data. This derivation could be shared with students in intermediate or advanced thermodynamics courses. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. Certain Geometric Study Involving the Barnes–Mittag-Leffler Function.
- Author
-
Alenazi, Abdulaziz and Mehrez, Khaled
- Subjects
GAMMA functions ,STAR-like functions ,UNIVALENT functions ,CONVEX functions ,ANALYTIC functions - Abstract
The main purpose of this paper is to study certain geometric properties of a class of analytic functions involving the Barnes–Mittag-Leffler function. The main mathematical tools are the monotonicity patterns of some class of functions associated with the gamma and digamma functions. Furthermore, some consequences and examples are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Some New Approaches to Fractional Euler–Maclaurin-Type Inequalities via Various Function Classes.
- Author
-
Gümüş, Mehmet, Hezenci, Fatih, and Budak, Hüseyin
- Subjects
FRACTIONAL integrals ,FRACTIONAL calculus ,CONVEX functions ,INTEGRAL functions - Abstract
This paper aims to examine an approach that studies many Euler–Maclaurin-type inequalities for various function classes applying Riemann–Liouville fractional integrals. Afterwards, our results are provided by using special cases of obtained theorems and examples. Moreover, several Euler–Maclaurin-type inequalities are presented for bounded functions by fractional integrals. Some fractional Euler–Maclaurin-type inequalities are established for Lipschitzian functions. Finally, several Euler–Maclaurin-type inequalities are constructed by fractional integrals of bounded variation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. Convergence of distributed approximate subgradient method for minimizing convex function with convex functional constraints.
- Author
-
Jedsadapong Pioon, Narin Petrot, and Nimit Nimana
- Subjects
SUBGRADIENT methods ,CONVEX functions - Abstract
In this paper, we investigate the distributed approximate subgradient-type method for minimizing a sum of differentiable and non-differentiable convex functions subject to nondifferentiable convex functional constraints in a Euclidean space. We establish the convergence of the sequence generated by our method to an optimal solution of the problem under consideration. Moreover, we derive a convergence rate of order O(N
1−a ) for the objective function values, where a ∈ (0.5, 1). Finally, we provide a numerical example illustrating the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
37. NONLINEAR STRICT CONE SEPARATION THEOREMS IN REAL NORMED SPACES.
- Author
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GÜNTHER, CHRISTIAN, KHAZAYEL, BAHAREH, and TAMMER, CHRISTIANE
- Subjects
NONLINEAR theories ,CONVEX functions ,CONES ,ALGEBRAIC functions ,REAL variables - Abstract
In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under weaker conditions (concerning convexity and closedness requirements) with respect to the involved cones. By a new characterization of the algebraic interior of augmented dual cones in real normed spaces, we are able to establish relationships between our cone separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim. 20) and by García-Castaño, Melguizo-Padial and Parzanese (2023, Math. Meth. Oper. Res. 97). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. AN INEXACT NONMONOTONE PROJECTED GRADIENT METHOD FOR CONSTRAINED MULTIOBJECTIVE OPTIMIZATION.
- Author
-
XIAOPENG ZHAO, HUIJIE ZHANG, and YONGHONG YAO
- Subjects
MULTIDISCIPLINARY design optimization ,STOCHASTIC convergence ,PARETO optimum ,CONVEX functions ,CONJUGATE gradient methods - Abstract
In this paper, we consider an inexact projected gradient method equipped with a nonmonotone line search rule for smooth constrained multiobjective optimization. In this method, a new nonmonotone line search technique proposed here is employed and the relative errors on the search direction is admitted. We demonstrate that this method is well-defined. Then, we prove that each accumulation point of the sequence generated by this method is Pareto stationary and analyze the convergence rate of the algorithm. When the objective function is convex, the convergence of the sequence to a weak Pareto optimal point of the problem is established. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Optimal energy decay for a viscoelastic Kirchhoff equation with distributed delay acting on nonlinear frictional damping.
- Author
-
Mohammed, Aili and Khemmoudj, Ammar
- Subjects
WAVE equation ,CONVEX functions ,EQUATIONS ,DELAY differential equations - Abstract
In this paper, we have analysed the influence of viscoelastic and frictional damping on the decay rate of solutions for a Kirchhoff-type viscoelastic wave equation with a distributed delay acting on nonlinear internal damping. Taking the relaxation function of a fairly large class and using the method of energy in which we introduce an adapted Lyapunov functional and by exploiting certain properties of convex functions, under certain assumptions on the constants of system, we obtain the optimal decay rate of energy in the sense that it is compatible with the decay rate of the relaxation function. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. Panoptic Segmentation with Convex Object Representation.
- Author
-
Yao, Zhicheng, Wang, Sa, Zhu, Jinbin, and Bao, Yungang
- Subjects
- *
DEEP learning , *COMPUTER vision , *OBJECT-oriented methods (Computer science) , *VECTORS (Calculus) , *CONVEX functions - Abstract
The accurate representation of objects holds pivotal significance in the realm of panoptic segmentation. Presently, prevalent object representation methodologies, including box-based, keypoint-based and query-based techniques, encounter a challenge known as the 'representation confusion' issue in specific scenarios, often resulting in the mislabeling of instances. In response, this paper introduces Convex Object Representation (COR), a straightforward yet highly effective approach to address this problem. COR leverages a CNN-based Euclidean Distance Transform to convert the target instance into a convex heatmap. Simultaneously, it offers a parallel embedding method for encoding the object. Subsequently, COR characterizes objects based on the distinctive embedding vectors of their convex vertices. This paper seamlessly integrates COR into a state-of-the-art query-based panoptic segmentation framework. Experimental findings validate that COR successfully mitigates the representation confusion predicament, enhancing segmentation accuracy. The COR-augmented methods exhibit notable improvements of +1.3 and +0.7 points in PQ on the Cityscapes validation and MS COCO panoptic 2017 validation datasets, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. REVERSE OSTROWSKI'S TYPE WEIGHTED INEQUALITIES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS.
- Author
-
DRAGOMIR, SILVESTRU SEVER, JLELI, MOHAMED, and SAMET, BESSEM
- Subjects
CONVEX functions ,VECTOR spaces ,NORMAL operators ,MATHEMATICAL inequalities ,LINEAR algebra ,POLYNOMIALS ,MATHEMATICAL formulas - Abstract
In this paper we provide several upper and lower bounds for the Ostrowski difference ... where f : C → R is a convex function, C is a convex subset of a vector space X and w is integrable and nonnegative a.e. on [0,1] . A perturbed version under some natural assumptions on the weight function w is also considered. These results are then employed to obtain several weighted integral inequalities for norms and semi-inner products. The particular case of inner product spaces is analyzed and refinements of the weighted integral midpoint inequality for norms are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Ostrowski type inequalities via ψ−(α,β,γ,δ)− convex function.
- Author
-
Hassan, Ali and Khan, Asif R.
- Subjects
INTEGRAL inequalities ,ABSOLUTE value - Abstract
In this paper, we are introducing very first time the class of (α, β, γ, δ)-convex function in mixed kind, which is the generalization of many classes of convex functions. We would like to state well-known Ostrowski inequal- ity via Montgomery identity for ψ - (α, β, γ, δ)-convex function in mixed kind. In addition, we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are ψ – (α, β, γ, δ)-convex functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. New classes of univalent functions using a new differential operator.
- Author
-
Aron, Mihai
- Abstract
In this paper we present new classes of univalent functions, or more generally, a new univalence criteria for normalized analytic functions, using an operator defined concerning to the idea behind a Marx–Strohhäcker type theorem. Also, we determine coefficient estimates and study Fekete–Szegö problem for these classes. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Fractional Euler-Maclaurin-type inequalities for various function classes.
- Author
-
Hezenci, Fatih and Budak, Hüseyin
- Abstract
This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Logarithmic coefficient bounds for the class of Bazilevič functions.
- Author
-
Sharma, Navneet Lal and Bulboacă, Teodor
- Abstract
If S denotes the class of all univalent functions in the open unit disk D : = z ∈ C : | z | < 1 with the form f (z) = z + ∑ n = 2 ∞ a n z n , then the logarithmic coefficients γ n of f ∈ S are defined by log f (z) z = 2 ∑ n = 1 ∞ γ n (f) z n , z ∈ D.
The logarithmic coefficients were brought to the forefront by I.M. Milin in the 1960’s as a method of calculating the coefficients a n for f ∈ S . He concerned himself with logarithmic coefficients and their role in the theory of univalent functions, while in 1965 Bazilevič also pointed out that the logarithmic coefficients are crucial in problems concerning the coefficients of univalent functions. In this paper we estimate the bounds for the logarithmic coefficients | γ n (f) | when f belongs to the class B (α , β) of Bazilevič function of type (α , β) . [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Some Simpson- and Ostrowski-Type Integral Inequalities for Generalized Convex Functions in Multiplicative Calculus with Their Computational Analysis.
- Author
-
Zhan, Xinlin, Mateen, Abdul, Toseef, Muhammad, and Aamir Ali, Muhammad
- Subjects
CONVEX functions ,CALCULUS ,GENERALIZED integrals ,INTEGRAL inequalities ,DIFFERENTIABLE functions ,NUMERICAL integration - Abstract
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]
- Published
- 2024
- Full Text
- View/download PDF
47. Sufficiency Conditions for a Class of Convex Functions Connected with Tangent Functions Associated with the Combination of Babalola Operators and Binomial Series.
- Author
-
El-Deeb, Sheza M. and Cotîrlă, Luminita-Ioana
- Subjects
TANGENT function ,CONVEX functions ,LOGARITHMIC functions - Abstract
In this paper, we create a new subclass of convex functions given with tangent functions applying the combination of Babalola operators and Binomial series. Moreover, we obtain several important geometric results, including sharp coefficient bounds, sharp Fekete–Szego inequality, Kruskal inequality, and growth and distortion estimates. Furthermore, for functions with logarithmic coefficients, we compute sharp Fekete–Szego inequality and sharp coefficient bounds. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
48. Some New f-Divergence Measures and Their Basic Properties.
- Author
-
Dragomir, Silvestru Sever
- Subjects
INTEGRAL inequalities ,CONVEX functions - Abstract
In this paper, we introduce some new f-divergence measures that we call t-asymmetric/symmetric divergence measure and integral divergence measure, establish their joint convexity and provide some inequalities that connect these f-divergences to the classical one introduced by Csiszar in 1963. Applications for the dichotomy class of convex functions are provided as well. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. Hermite-Hadamard Inequalities for Generalized (m - F)-Convex Function in the Framework of Local Fractional Integrals.
- Author
-
RAZZAQ, ARSLAN, JAVED, IRAM, V., JUAN E. NÁPOLES, and GONZÁLEZ, FRANCISCO MARTÍNEZ
- Subjects
FRACTIONAL integrals ,FRACTIONAL calculus ,FRACTALS ,INTEGRAL inequalities ,DIFFERENTIABLE functions ,CALCULUS - Abstract
This work presents new versions of the Hermite-Hadamard Inequality, for (m-F)-convex functions, defined on fractal sets R ς (0 < ς ≤ 1). So, we show some new results for twice differentiable functions using local fractional calculus, as well as some new definitions. We will construct these new integral inequality using the generalized Hölder-integral inequality and the power mean integral inequality. Furthermore, we present some new inequalities for the midpoint and trapezoid formulas in a novel type of fractal calculus. The conclusions in this paper are substantial advancements and generalizations of prior research reported in the literature. 2020 Mathematics Subject Classification. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. Generalized Euclidean operator radius.
- Author
-
Alomari, Mohammad W., Sababheh, Mohammad, Conde, Cristian, and Moradi, Hamid Reza
- Subjects
HILBERT space ,CONVEX functions ,GENERALIZATION ,RADIUS (Geometry) - Abstract
In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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