Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (2): 589-599.doi: 10.1016/S0252-9602(13)60022-3

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MULTI-VALUED TOTALLY QUASI-Φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES

 ZHANG Shi-Sheng*, WANG Lin, ZHAO Yun-He   

  1. College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
  • Received:2012-03-05 Revised:2012-10-26 Online:2013-03-20 Published:2013-03-20
  • Contact: ZHANG Shi-Sheng,changss@yahoo.cn E-mail:changss@yahoo.cn; wl64mail@yahoo.com.cn; zyh961019@163.com
  • Supported by:

    This work was supported by the Natural Science Foundation of Yunnan Province (2011FB074).

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

CLC Number: 

  • 47J05
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