Some extragradient methods for common solutions of generalized equilibrium problems and fixed points of nonexpansive mappings

Fixexd point theory and applications

Jian-Wen Peng¹ 

[1] School of Mathematics, Chongqing Normal University, Chongqing, PR China

关键词: Generalized equilibrium problem;    Extragradient method;    Hybrid method;    Nonex-pansive mapping;    Strong convergence;    Weak convergence;   

DOI  :  10.1186/1687-1812-2011-12

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we introduce some new iterative schemes based on the extragradient method (and the hybrid method) for finding a common element of the set of solutions of a generalized equilibrium problem, and the set of fixed points of a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for a monotone, Lipschitz-continuous mapping in Hilbert spaces. We obtain some strong convergence theorems and weak convergence theorems. The results in this article generalize, improve, and unify some well-known convergence theorems in the literature.

【 授权许可】

CC BY