Acta mathematica scientia, Series B >
MULTI-VALUED TOTALLY QUASI-Φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES
Received date: 2012-03-05
Revised date: 2012-10-26
Online published: 2013-03-20
Supported by
This work was supported by the Natural Science Foundation of Yunnan Province (2011FB074).
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
ZHANG Shi-Sheng , WANG Lin , ZHAO Yun-He . MULTI-VALUED TOTALLY QUASI-Φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2013 , 33(2) : 589 -599 . DOI: 10.1016/S0252-9602(13)60022-3
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