(untitled) (Communications in Mathematical Research, 2021)
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.