Strong Convergence Theorems for a Countable Family of Total Quasi- ϕ -Asymptotically Nonexpansive Nonself Mappings

Abstract

The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.