关键词: Multi-valued totally Quasi-Φ-asymptotically nonexpansive semi-groups, mod-ified Halpern-Mann-type iteration, multi-valued quasi-Φ-symptotically nonex-pansive semi-groups, multi-valued quasi-Φ-nonexpansive semi-groups, multi-valued relatively nonexpansive semi-groups, generalized projection

Abstract:

The purpose of this article is first to introduce the concept of multi-valued to-tally Quasi-Φ-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 Quasi-Φ-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.

Key words: Multi-valued totally Quasi-Φ-asymptotically nonexpansive semi-groups, mod-ified Halpern-Mann-type iteration, multi-valued quasi-Φ-symptotically nonex-pansive semi-groups, multi-valued quasi-Φ-nonexpansive semi-groups, multi-valued relatively nonexpansive semi-groups, generalized projection