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Title: Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces
Authors: Li, XS
Yip, TL 
Issue Date: 11-Sep-2012
Source: Fixed point theory and applications, Sept. 2012, 2012:145
Abstract: In this paper, we study the convergence of implicit Mann iteration processes with bounded perturbations for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the Δ-convergence results of implicit Mann iteration schemes with bounded perturbations for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Mann iteration schemes with bounded perturbations for nonexpansive semigroups in CAT(0) spaces. The results presented in this paper extend and enrich the existing literature.
MSC: 47H05; 47H10; 47J25
Keywords: Common fixed point
Δ-convergence
Nonexpansive semigroup
CAT (0) space
Implicit approximation
Publisher: Springer
Journal: Fixed point theory and applications 
ISSN: 1687-1820
EISSN: 1687-1812
DOI: 10.1186/1687-1812-2012-145
Rights: © 2012 Li and Yip; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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