Iterative approximation methods for mixed equilibrium problems for a countable family of quasi- ? -asymptotically nonexpansive multivalued mappings in Banach spaces

摘要

In this paper, we prove the existence of a solution of the mixed equilibrium problem MEP ( f , φ , C ) by using the KKM mapping in a Banach space setting. Then, by virtue of this result, we introduce a hybrid iterative scheme for finding a common element of the set of solutions of MEP ( f , φ , C ) and the set of common fixed points of a countable family of quasi-?-asymptotically nonexpansive multivalued mappings. Furthermore, we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of MEP ( f , φ , C ) and the set of common fixed points of a countable family of quasi-?-asymptotically nonexpansive multivalued mappings.