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Some new fractional integral inequalities for exponentially m-convex functions via extended generalized mittag-Leffler function

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2019年第1期2019卷 1-17页

作者： Rashid, Saima Safdar, Farhat Akdemir, Ahmet Ocak Noor, muhammad Aslam Noor, Khalida Inayat Govt Coll GC Univ Faisalabad Pakistan Sardar Bahadur Khan Womens Univ Quetta Pakistan Ibrahim Cecen Univ Agri Fac Sci & Letters Dept Math Agri Turkey COMSATS Univ Islamabad Dept Math Islamabad Pakistan

In the article, we establish some new general fractional integral inequalities for exponentially m-convex functions involving an extended mittag-Leffler function, provide several kinds of fractional integral operator ... 详细信息

关键词： convex function Exponentially convex function m-convex function mittag-Leffler function Generalized fractional integral operator Hermite-Hadamard inequality

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General fractional integral inequalities for convex and m-convex functions via an extended generalized mittag-Leffler function

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2018年第1期2018卷 243-243页

作者： Farid, G. Khan, K. A. Latif, N. Rehman, A. U. mehmood, S. COMSATS Univ Islamabad Dept Math Attock Pakistan Univ Sargodha Dept Math Sargodha Pakistan Jubail Ind Coll Gen Studies Dept Jubail Ind City Saudi Arabia GBPS Sherani Hazro Attock Pakistan

In this paper some new general fractional integral inequalities for convex and m-convex functions by involving an extended mittag-Leffler function are presented. These results produce inequalities for several kinds of... 详细信息

关键词： convex function m-convex function mittag-Leffler function Generalized fractional integral operators Hadamard inequality

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A study of Hermite-Hadamard inequalities via Caputo-Fabrizio fractional integral operators using strongly (s,m)-convex functions in the second sense

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2025年第1期2025卷 1-24页

作者： Li, Jie Lin, Yong Ozcan, Serap Saleem, muhammad Shoaib Shah, Ahsan Fareed Suzhou Univ Fac Math & Stat Suzhou 234000 Anhui Peoples R China Suzhou Univ Fac Mech & Elect Engn Suzhou 234000 Anhui Peoples R China Kirklareli Univ Fac Arts & Sci Dept Math Kirklareli Turkiye Univ Okara Dept Math Okara 56300 Pakistan Khazar Univ Ctr Theoret Phys 41 Mehseti St Baku AZ1096 Azerbaijan FGEID C G Fac Math Okara Pakistan

New ways for comparing and bounding strongly (s,m)-convex functions using Caputo fractional derivatives and Caputo-Fabrizio integral operators are explored. These operators generalize some classic inequalities of Hermite-Hadamard for functions with strongly (s,m)-convex derivatives. The findings are also applied to special functions and means involving the digamma function. Additionally, we relate our findings to applications in biomedicine, engineering, robotics, the automotive industry, and electronics.

关键词： convex function s-convex function m-convex function Strongly convex function Hermite-Hadamard inequality Caputo-Fabrizio fractional integrals

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m-convex functions and tree metrics

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED mATHEmATICS 2004年第3期21卷 391-403页

作者： Hirai, H murota, K Kyoto Univ Math Sci Res Inst Kyoto 6068502 Japan Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Tokyo 1138656 Japan

We reveal a close relationship between quadratic m-convex functions and tree metrics: A quadratic function defined on the integer lattice points is m-convex if and only if it has a tree representation. Furthermore, a discrete analogue of the Hessian matrix is defined for functions on the integer points. A function is m-convex if and only if the negative of the 'discrete Hessian matrix' is a tree metric matrix at each integer point. Thus, the m-convexity of a function can be characterized by that of its local quadratic approximations.

关键词： m-convex function tree metric four-point condition discrete Hessian matrix

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A note on m-convex functions on jump systems

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DISCRETE APPLIED mATHEmATICS 2021年 289卷 492-502页

作者： murota, Kazuo Tokyo Metropolitan Univ Dept Econ & Business Adm Tokyo 1920397 Japan

A jump system is defined as a set of integer points (vectors) with a certain exchange property, generalizing the concepts of matroids, delta-matroids, and base polyhedra of integral polymatroids (or submodular systems). A discrete convexity concept is defined for functions on constant-parity jump systems and it has been used in graph theory and algebra. In this paper we call it "jump m-#-convexity" and extend it to "jump mbconvexity" for functions defined on a larger class of jump systems. By definition, every jump m-convex function is a jump m-#-convex function, and we show the equivalence of these concepts by establishing an (injective) embedding of jump mb-convex functions in n variables into the set of jump m-#-convex functions in n + 1 variables. Using this equivalence we show further that jump m-#-convex functions admit a number of natural operations such as aggregation, projection (partial minimization), convolution, composition, and transformation by a network. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Discrete convex analysis Jump system m-convex function

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Operations on m-convex functions on jump systems

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SIAm JOURNAL ON DISCRETE mATHEmATICS 2007年第1期21卷 107-129页

作者： Kobayashi, Yusuke murota, Kazuo Tanaka, Ken'Ichiro Univ Tokyo Grad Sch Informat Sci & Technol Tokyo 1138656 Japan

A jump system is a set of integer points with an exchange property, which is a generalization of a matroid, a delta-matroid, and a base polyhedron of an integral polymatroid (or a submodular system). Recently, the concept of m-convex functions on constant-parity jump systems was introduced by murota as a class of discrete convex functions that admit a local criterion for global minimality. m-convex functions on constant-parity jump systems generalize valuated matroids, valuated delta-matroids, and m-convex functions on base polyhedra. This paper reveals that the class of m-convex functions on constant-parity jump systems is closed under a number of natural operations such as splitting, aggregation, convolution, composition, and transformation by networks. The present results generalize hitherto-known similar constructions for matroids, delta-matroids, valuated matroids, valuated delta-matroids, and m- convex functions on base polyhedra.

关键词： jump system m-convex function aggregation convolution transformation by networks

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Induction of m-convex functions by linking systems

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DISCRETE APPLIED mATHEmATICS 2007年第11期155卷 1471-1480页

作者： Kobayashi, Yusuke murota, Kazuo Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Tokyo 1138656 Japan

Induction (or transformation) by bipartite graphs is one of the most important operations on matroids, and it is well known that the induction of a matroid by a bipartite graph is again a matroid. As an abstract form of this fact, the induction of a matroid by a linking system is known to be a matroid. m-convex functions are quantitative extensions of matroidal structures, and they are known as discrete convex functions. As with matroids, it is known that the induction of an m-convex function by networks generates an m-convex function. As an abstract form of this fact, this paper shows that the induction of an m-convex function by linking systems generates an m-convex function. Furthermore, we show that this result also holds for m-convex functions on constant-parity jump systems. Previously known operations such as aggregation, splitting, and induction by networks can be understood as special cases of this construction. (c) 2007 Elsevier B.V. All rights reserved.

关键词： m-convex function jump system linking system

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New characterizations of m-convex functions and their applications to economic equilibrium models with indivisibilities

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DISCRETE APPLIED mATHEmATICS 2003年第2期131卷 495-512页

作者： murota, K Tamura, A Univ Tokyo Grad Sch Informat Sci & Technol Tokyo 1138656 Japan Kyoto Univ Math Sci Res Inst Kyoto 6068502 Japan

The concept of m-convex functions plays a central role in "discrete convex analysis", a unified framework of discrete optimization recently developed by murota and others. This paper gives two new characterizations of m- and W-convex functions generalizing Gul and Stacchetti's results on the equivalence among the single improvement condition, the gross substitutes condition and the no complementarities condition for set functions (utility functions on {0, 1} vectors) as well as Fujishige and Yang's observation on the connection to m-convexity. We also discuss implications of our results in an exchange economy with indivisible goods. (C) 2003 Elsevier B.V. All rights reserved.

关键词： m-convex function m/natural-convex function exchange economy indivisibility

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A survey of fundamental operations on discrete convex functions of various kinds

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OPTImIZATION mETHODS & SOFTWARE 2021年第2-3期36卷 472-518页

作者： murota, Kazuo Tokyo Metropolitan Univ Dept Econ & Business Adm Tokyo Japan

Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to offer a survey on fundamental operations for various kinds of discrete convex functions in discrete convex analysis such as integrally convex functions, L-convex functions, m-convex functions, and multimodular functions.

关键词： Discrete convex analysis integrally convex function L-convex function m-convex function multimodular function submodular function valuated matroid

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Congestion games viewed from m-convexity

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OPERATIONS RESEARCH LETTERS 2015年第3期43卷 329-333页

作者： Fujishige, Satoru Goemans, michel Harks, Tobias Peis, Britta Zenklusen, Rico Kyoto Univ Math Sci Res Inst Kyoto 6068502 Japan MIT Dept Math Cambridge MA 02139 USA Maastricht Univ Sch Business & Econ Dept Quantitat Econ NL-6200 MD Maastricht Netherlands Rhein Westfal TH Aachen Sch Business & Econ D-52072 Aachen Germany Swiss Fed Inst Technol Dept Math Inst Operat Res CH-8092 Zurich Switzerland

Congestion games have extensively been studied till recently. It is shown by Fotakis (2010) that for every congestion game on an extension-parallel network, any best-response sequence reaches a pure Nash equilibrium of the game in n steps, where n is the number of players. We show that the fast convergence of best-response sequences results from m-convexity (of murota (1996)) of the potential function associated with the game. We also give a characterization of m-convex functions in terms of greedy algorithms. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Congestion games Discrete convexity Best-response dynamics m-convex function Discrete convexity

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