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

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 Δ-convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) sp...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.41-48-605
Main Authors: Liu, Zhi-bin, Chen, Yi-shen, Li, Xue-song, Xiao, Yi-bin
Format: Article
Language:English
Subjects:
Approximation theory
Convergence (Mathematics)
Mathematical research
Sequences (Mathematics)
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Summary: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 Δ-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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/503198