Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi‐ϕ‐Asymptotically Nonexpansive Mappings in Banach Spaces
Jinhua Zhu, Shih-sen Chang, Min Liu · Journal of Applied Mathematics · 2011
The purpose of this paper is first to introduce the concept of total quasi‐ϕ‐asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi‐ϕ‐asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec‐Klee property. The results presented in the paper improve and extend some recent results.