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

Fixed Point Theory and Applications

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

DOI  :  

来源: DOAJ

【 摘 要 】

Abstract

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】

Unknown