Iterative approximation methods for mixed equilibrium problems for a countable family of quasi-ϕ-asymptotically nonexpansive multivalued mappings in Banach spaces
Rabian Wangkeeree, Pakkapon Preechasilp · Fixed Point Theory and Applications · 2013
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-φ-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-φ-asymptotically nonexpansive multivalued mappings.