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STRONG CONVERGENCE THEOREMS FOR equilibrium problem AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES

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Acta Mathematica Scientia 2016年第5期36卷 1433-1444页

作者：朱胜黄建华 Institute of Mathematics and Computer Science Fuzhou University Fuzhou 350002 China

In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.

关键词： equilibrium problem Bregman totally quasi-asymptotically nonexpansive mapping Bregman distance reflexive Banach space

Viscosity approximation with weak contractions for fixed point problem,equilibrium problem,and variational inequality problem

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Applied Mathematics and Mechanics(English Edition) 2010年第10期31卷 1273-1282页

作者：张石生李向荣陈志坚柳京爱 Department of Mathematics Yibin University Department of Applied Mathematics The Hong Kong Polytechnic University Department of Mathematics and Physics Beijing Institute of Petrochemical Technology

This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak *** purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational *** suitable conditions,some strong convergence theorems are established in the framework of Hilbert *** results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,*** implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive *** Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,*** Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert ***.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,*** iterative method for finding common solutions of equilibrium problem and fixed point ***.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,*** theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive *** Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.

关键词： viscosity approximation weak contraction mapping equilibrium problem nonexpansive mapping implicit iteration minimization problem

A HYBRID VISCOSITY APPROXIMATION METHOD FOR A COMMON SOLUTION OF A GENERAL SYSTEM OF VARIATIONAL INEQUALITIES,AN equilibrium problem,AND FIXED POINT problemS

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Journal of Computational Mathematics 2023年第1期41卷 153-172页

作者： Maryam Yazdi Saeed Hashemi Sababe Young Researchers and Elite Club Malard BranchIslamic Azad UniversityMalardIran Department of mathematical and statistical sciences University of AlbertaEdmontonCanada Young Researchers and Elite ClubMalard BranchIslamic Azad UniversityMalardIran

In this paper,we introduce a new iterative method based on the hybrid viscosity approximation method for finding a common element of the set of solutions of a general system of variational inequalities,an equilibrium problem,and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert *** prove a strong convergence theorem of the proposed iterative scheme under some suitable conditions on the ***,we apply our main result for ***,we give two numerical results to show the consistency and accuracy of the scheme.

关键词： equilibrium problem Iterative method Fixed point Variational inequality

equilibrium problemS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES

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Acta Mathematica Scientia 2005年第4期25卷 658-662页

作者：丁协平 College of Mathematics and Software Science Sichuan Normal University Chengdu 610066 China

By employing a fixed point theorem due to Ding, Park and Jung, some existence theorems of solutions for equilibrium problems with lower and upper bounds are proved in noncompact topological spaces. These results furth... 详细信息

关键词： equilibrium problem fixed point theorem contractible space acyclic space,topological space

WEAK CONVERGENCE THEOREMS FOR GENERAL equilibrium problemS AND VARIATIONAL INEQUALITY problemS AND FIXED POINT problemS IN BANACH SPACES

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Acta Mathematica Scientia 2013年第1期33卷 303-320页

作者：蔡钢步尚金 Department of Mathematical Sciences Tsinghua University

In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.

关键词： weak convergence relatively nonexpansive mapping equilibrium problem variational inequality

SOME RESULTS ON GENERALIZED equilibrium problemS INVOLVING STRICTLY PSEUDOCONTRACTIVE MAPPINGS

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Acta Mathematica Scientia 2011年第5期31卷 2041-2057页

作者： Jong Kyu Kim Sun Young Cho Department of Mathematics Educations Kyungnam UniversityMasan 631-701Korea Department of Mathematics Gyeongsang National UniversityChinju 660-701Korea

In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive *** show that the iterative sequence converges strongly to a common element of the solution set of ge... 详细信息

关键词： equilibrium problem nonexpansive mapping inverse-strongly monotone mapping strictly pseudocontractive mapping

CONVERGENCE ANALYSIS FOR SYSTEM OF equilibrium problemS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

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Acta Mathematica Scientia 2014年第4期34卷 1081-1097页

作者： Yekini SHEHU Department of Mathematics University of NigeriaNsukkaNigeria

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.

关键词： left Bregman strongly relatively nonexpansive mapping left Bregman projection equilibrium problem Banach spaces

Vectorial Ekeland variational principle for systems of equilibrium problems and its applications

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Science China Mathematics 2017年第7期60卷 1259-1280页

作者： QIU JingHui School of Mathematical Sciences Soochow University Suzhou 215006 China

For a family of vector-valued bifunctions,we introduce the notion of sequentially lower monotonity,which is strictly weaker than the lower semi-continuity of the second variables of the ***,we give a general version of vectorial Ekeland variational principle(briefly,denoted by EVP) for a system of equilibrium problems,where the sequentially lower monotone objective bifunction family is defined on products of sequentially lower complete spaces(concerning sequentially lower complete spaces,see Zhu et al(2013)),and taking values in a quasi-ordered locally convex ***,the perturbation consists of a subset of the ordering cone and a family {p_i}_(i∈I) of negative functions satisfying for each i∈I,p_i(x_i,y_i) = 0 if and only if x_i=y_*** the general version,we can deduce several particular equilibrium versions of EVP,which can be applied to show the existence of solutions for countable systems of equilibrium *** particular,we obtain a general existence result of solutions for countable systems of equilibrium problems in the setting of sequentially lower complete *** weakening the compactness of domains and the lower semi-continuity of objective bifunctions,we extend and improve some known existence results of solutions for countable system of equilibrium problems in the setting of complete metric spaces(or Fréchet spaces).When the domains are non-compact,by using the theory of angelic spaces(see Floret(1980)),we generalize some existence results on solutions for countable systems of equilibrium problems by extending the framework from reflexive Banach spaces to the strong duals of weakly compactly generated spaces.

关键词： Ekeland variational principle equilibrium problem system of equilibrium problems quasi-ordered locally convex space angelic space sequentially lower complete space

AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND equilibrium problemS

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Analysis in Theory and Applications 2009年第4期25卷 381-400页

作者： C.Jaiboon P.Kumam U.W.Humphries King Mongkut's University of Technology Thonburi Thailand

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.

关键词： nonexpansive mapping relaxed cocoercive mapping variational inequality,fixed point equilibrium problem extragradient method