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

Abstract

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

Keywords

• Banach space
• Fixed point
• Metric projection
• Generalized equilibrium problem
• Nonexpansive mapping