Abstract
The purpose of this article is first to introduce the concept of multi-valued totally Quasiϕ-asymptotically nonexpansive semi-groups, which contains many kinds of semi-groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasiϕ-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.
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