Strong Convergence for a Countable Family of Total Quasi-$ϕ$-Asymptotically Nonexpansive Nonself Mappings in Banach Space

Abstract

The purpose of this article is to introduce a class of total quasi-$ϕ$-asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-$ϕ$-asymptotically nonexpansive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this article extend and improve the corresponding results of many authors.