河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
中国期刊方阵入选期刊
中国高校优秀科技期刊
华北优秀期刊
河北省优秀科技期刊

协同采编系统

友情链接

Hilbert空间中均衡问题、不动点问题和变分不等式的新迭代算法

河北经贸大学数学与统计学学院, 河北石家庄 050061
DOI： 10.13763/j.cnki.jhebnu.nse.2015.01.004

A New Interative Method for Equilibrium Problems, Fixed Point Problems and Variational Ineqalities in Hilbert Space

DUAN Liling, LIU Yuanxing

PDF
下载
HTML

摘要/Abstract

摘要：

在Hilbert空间中,构造了一种新的迭代算法,并证明了迭代序列强收敛到一类均衡问题的解集、非扩展映射和严格伪压缩映射的不动点集及含有α逆强单调算子的变分不等式的解集的公共元.推广和补充了以往的相关研究成果.

Abstract：

In this paper, we propose a new iterative method for approximating the common element of the set of solutions of an equilibrium problem, the set of fixed points of non-expansive mappings and strictly pseudo-contractive mappings and the set of solutions of a variational inequalities for an α-inverse-strongly monotone operator in a Hilbert space. We prove some strong convergence theorems, which extend previous works in the literature.

关键词

关键词： 逆强单调算子 ; 非扩展映射 ; 严格伪压缩映射 ; 均衡问题 ; 变分不等式

Key words： inverse-strongly monotone operator ; nonexpansive mapping ; strictly pseudo-contractive mapping ; equilibrium problem ; variational inequality

参考文献 9

[1] IIDUKA H,TAKAHASHI W.Strong Convergence Theorems for Nonexpansive Mappings and Inverse-strongly Monotone Mappings[J].Nonlinear Anal,2005,61:341-350.
[2] MARNO G,XU H K.A General Iterative Method for Nonexpansive Mappings in Hilbert Space[J].J Math Anal Appl,2006,318:43-52.
[3] ZHOU H Y.Convergence Theorems of Fixed Points for K-strict Pseudo-contractions in Hilbert Spaces[J].Nonlinear Anal,2008,69:456-462.
[4] SU Y F,SHANG M J,QIN X L.An Iterative Method of Solution for Equilibrium and Optimization Problems[J].Nonlinear Anal,2008,64:140-152.
[5] LIU Y.A General Iterative Method for Equilibrium Problems and Strickly Pesudo-contractions in Hilbert Spaces[J].Nonlinear Anal,2009,71(10):4852-4861.
[6] BLUM E,OETTLI W.From Optimization and Variational Inequalities to Equilibrium Problems[J].Math Student,1994,63:123-145.
[7] FLAM S D,ANTIPIN A S.Equilibrium Programming Using Proximal-like Algorithms[J].Math Program,1997,78:29-41.
[8] BROWER F E,PETRYSHYN W V.Construction of Fixed Points of Nonlinear Mappings in Hilbert Space[J].J Math Anal Appl,1967,20:197-228.
[9] XU H K.Iterative Algorithms for Nonlinear Operators[J].J London Math Soc,2002,66:240-256.