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