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Subharmonic functions with Separated Variables and Their Connection with generalized convex functions

RUSSIAN MATHEMATICS 2024年第6期68卷 42-57页

作者： Muryasov, R. R. Russian Acad Sci Inst Math Comp Ctr Subdiv Ufa Fed Res Ctr Ufa 450008 Russia

In this paper, we consider the necessary and sufficient conditions for the subharmonicity of functions of two variables representable as a product of two functions of one variable in the Cartesian coordinate system or in the polar coordinate system in domains on the plane. We establish a connection of such functions with functions that are convex with respect to solutions of second-order linear differential equations, that is, convex with respect to two functions.

关键词： subharmonic function generalized derivative distribution convex function differential operator generalized convex function

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A UNIFIED APPROACH TO SOME INEQUALITIES FOR generalized convex functionS ON FRACTAL SETS AND THEIR APPLICATIONS

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR functionAL ANALYSIS 2018年 2018卷

作者： Sun, Wenbing Shaoyang Univ Sch Sci Shaoyang 422000 Hunan Peoples R China

In this paper, a general local fractional integral identity on fractal set R-alpha (0 < alpha <= 1) is established. We obtain some general local fractional integral inequalities for twice differentiable generalized convex functions. Based on these results, we derive some special inequalities. Some applications to error estimations for numerical integration and to special means are also given.

关键词： Fractal space Local fractional integral Hadamard's inequality generalized convex function Integral inequality

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Nondifferentiable fractional semi-infinite multiobjective optimization problems

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OPERATIONS RESEARCH LETTERS 2016年第2期44卷 260-266页

作者： Thai Doan Chuong Univ New S Wales Sch Math & Stat Sydney NSW 2052 Australia

Employing some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for local (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization problem with an infinite number of inequality constraints. Sufficient conditions for such solutions to the considered problem are also obtained by means of proposing the use of (strictly) generalized convex functions. In addition, we state a dual problem to the primal one and explore duality relations. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Fractional semi-infinite multiobjective programming Optimality condition Duality Limiting subdifferential generalized convex function

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Optimality Conditions for generalized convex Nonsmooth Uncertain Multi-objective Fractional Programming

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Journal of the Operations Research Society of China 2023年第4期11卷 809-826页

作者： Xiao Pan Guo-Lin Yu Tian-Tian Gong School of Mathematics and Information Science North Minzu UniversityYinchuan750021NingxiaChina

This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are *** optimality conditions are obtained under pseudo-quasi-type-I generalized convexity ***,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle *** main results in the present paper are verified by concrete examples.

关键词： Multi-objective fractional programming Robust weak efficient solution generalized convex function Optimality condition Saddle point

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An extension of the proximal point algorithm beyond convexity

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JOURNAL OF GLOBAL OPTIMIZATION 2022年第2期82卷 313-329页

作者： Grad, Sorin-Mihai Lara, Felipe Univ Vienna Fac Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria Univ Tarapaca Fac Ciencias Dept Matemat Arica Chile

We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly convex, and DC (difference of convex) functions that are prox-convex, however none of these classes fully contains the one of prox-convex functions or is included into it. We show that the classical proximal point algorithm remains convergent when the convexity of the proper lower semicontinuous function to be minimized is relaxed to prox-convexity.

关键词： Nonsmooth optimization Nonconvex optimization Proximity operator Proximal point algorithm generalized convex function

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θ-MONOTONE OPERATORS AND θ-convex functionS

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TAIWANESE JOURNAL OF MATHEMATICS 2012年第2期16卷 733-759页

作者： Laszlo, Szilard Univ Babes Bolyai Fac Math & Comp Sci Cluj Napoca 400084 Romania

In this paper we introduce a new monotonicity concept for multivalued operators, respectively, a new convexity concept for real valued functions, which generalize several monotonicity, respectively, convexity notions already known in literature. We present some fundamental properties of the operators having this monotonicity property. We show that if such a monotonicity property holds locally then the same property holds globally on the whole domain of the operator. We also show that these two new concepts are closely related. As an immediate application we furnish some surjectivity results in finite dimensional spaces.

关键词： generalized monotone operator Maximal monotonicity Locally monotone operator generalized convex function

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Some new local fractional inequalities associated with generalized (s,m)-convex functions and applications

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ADVANCES IN DIFFERENCE EQUATIONS 2020年第1期2020卷 1-27页

作者： Abdeljawad, Thabet Rashid, Saima Hammouch, Zakia Chu, Yu-Ming Prince Sultan Univ Dept Math & Gen Sci Riyadh Saudi Arabia China Med Univ Taiwan Dept Med Res Taichung Taiwan Asia Univ Dept Comp Sci & Informat Engn Taichung Taiwan Govt Coll Univ Dept Math Faisalabad Pakistan Moulay Ismail Univ Meknes Fac Sci & Tech Errachidia Morocco Huzhou Univ Dept Math Huzhou Peoples R China Changsha Univ Sci & Technol Hunan Prov Key Lab Math Modeling & Anal Engn Changsha Peoples R China

Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive field of research. The fractal sets are the effective tools to describe the accuracy of the inequalities for convex functions. In this paper, we employ linear fractals R alpha to investigate the (s,m)-convexity and relate them to derive generalized Hermite-Hadamard (HH) type inequalities and several other associated variants depending on an auxiliary result. Under this novel approach, we aim at establishing an analog with the help of local fractional integration. Meanwhile, we establish generalized Simpson-type inequalities for (s,m)-convex functions. The results in the frame of local fractional showed that among all comparisons, we can only see the correlation between novel strategies and the earlier consequences in generalized s-convex, generalized m-convex, and generalized convex functions. We obtain application in probability density functions and generalized special means to confirm the relevance and computational effectiveness of the considered method. Similar results in this dynamic field can also be widely applied to other types of fractals and explored similarly to what has been done in this paper.

关键词： generalized convex function generalized s-convex function Hermite-Hadamard inequality Simpson-type inequality generalized m-convex functions Fractal sets 26E60

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Some new Simpson-type inequalities for generalizedp-convex function on fractal sets with applications

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ADVANCES IN DIFFERENCE EQUATIONS 2020年第1期2020卷 1-26页

作者： Abdeljawad, Thabet Rashid, Saima Hammouch, Zakia Iscan, Imdat Chu, Yu-Ming Prince Sultan Univ Dept Math & Gen Sci Riyadh Saudi Arabia China Med Univ Dept Med Res Taichung Taiwan Asia Univ Dept Comp Sci & Informat Engn Taichung Taiwan Govt Coll Univ Dept Math Faisalabad Pakistan Univ Moulay Ismail Fac Sci & Tech Dept Math Errachidia Morocco Giresun Univ Fac Arts & Sci Dept Math Giresun Turkey Huzhou Univ Dept Math Huzhou Peoples R China Changsha Univ Sci Technol Hunan Prov Key Lab Math Modeling & Anal Engn Changsha Peoples R China

The present article addresses the concept ofp-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers arep-convex. The method we present is an alternative in showing the classical variants associated with generalizedp-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

关键词： generalized convex function generalizeds-convex function Hermite-Hadamard inequality Simpson's-like type inequality generalizedm-convex functions Fractal sets

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Genuine Bernstein-Durrmeyer type operators preserving 1 and x^j

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ANNALS OF functionAL ANALYSIS 2024年第1期15卷 1-22页

作者： Abel, Ulrich Acu, Ana Maria Heilmann, Margareta Rasa, Ioan Tech Hsch Mittelhessen Fachbereich MND Giessen Germany Lucian Blaga Univ Sibiu Dept Math & Informat Sibiu Romania Univ Wuppertal Sch Math & Nat Sci Wuppertal Germany Tech Univ Cluj Napoca Dept Math Cluj Napoca Romania

We introduce a family of genuine Bernstein-Durrmeyer type operators preserving the functions 1 and x(j). For them, we establish Voronovskaja type formulas. The behaviour with respect to generalized convex functions is... 详细信息

关键词： Genuine Bernstein-Durrmeyer operator Aldaz-Kounchev-Render operator Voronovskaya type formulas generalized convex function

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An approach of majorization in spaces with a curved geometry

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2014年第1期411卷 119-128页

作者： Niculescu, Constantin P. Roventa, Ionel Univ Craiova Dept Math Craiova 200585 Romania

The Hardy-Littlewood-Polya majorization theorem is extended to the framework of some spaces with a curved geometry (such as the global NPC spaces and the Wasserstein spaces). We also discuss the connection between our concept of majorization and the subject of Schur convexity. Several applications are included. (C) 2013 Elsevier Inc. All rights reserved.

关键词： generalized convex function Global NPC space Majorization of measures Wasserstein distance

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