Existence and iterative approximation for generalized equilibrium problems for a countable family of nonexpansive mappings in banach spaces

Fixexd point theory and applications

Rabian Wangkeeree¹  Uthai Kamraksa¹ 

[1] Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand

关键词: Banach space;    Fixed point;    Metric projection;    Generalized equilibrium problem;    Nonexpansive mapping;   

DOI  :  10.1186/1687-1812-2011-11

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of countable family of nonexpansive mappings in the frameworks of Banach spaces. By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings. AMS Subject Classification: 47H09, 47H10.

【 授权许可】

CC BY