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Abstract and Applied Analysis
Volume 2013, Article ID 503198, 8 pages
Research Article

Implicit Ishikawa Approximation Methods for Nonexpansive Semigroups in CAT(0) Spaces

1Southwest Petroleum University, Chengdu 610500, China
2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu 610500, China
3China Petroleum Engineering and Construct Corporation, Beijing 100120, China
4Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
5School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Received 29 November 2012; Accepted 12 June 2013

Academic Editor: Mohamed Amine Khamsi

Copyright © 2013 Zhi-bin Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the -convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results.