Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces

Xue Song Li; Tsz Leung Yip

doi:10.1186/1687-1812-2012-145

Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces

Research output: Journal article publication › Journal article › Academic research › peer-review

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.

Original language	English
Article number	145
Journal	Fixed Point Theory and Applications
Volume	2012
DOIs	https://doi.org/10.1186/1687-1812-2012-145
Publication status	Published - 1 Jan 2012

Keywords

CAT(0) space
Common fixed point
Implicit approximation
Nonexpansive semigroup
Δ-convergence

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

More information

10.1186/1687-1812-2012-145

http://hdl.handle.net/10397/5417

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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.",

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AB - 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.

KW - CAT(0) space

KW - Common fixed point

KW - Implicit approximation

KW - Nonexpansive semigroup

KW - Δ-convergence

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JO - Fixed Point Theory and Applications

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M1 - 145

ER -

Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces

Abstract

Keywords

ASJC Scopus subject areas

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