Strong convergence of a general iteration scheme in CAT(0) spaces

Abdul Rahim Khan; Mohamed Amine Khamsi; Hafiz Fukhar-Ud-Din

doi:10.1016/j.na.2010.09.029

Strong convergence of a general iteration scheme in CAT(0) spaces

Abdul Rahim Khan, Mohamed Amine Khamsi, Hafiz Fukhar-Ud-Din

Research output: Contribution to journal › Article › peer-review

75 Scopus citations

Abstract

We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and CAT(0) spaces. The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step iteration scheme of Xu and Noor and the scheme of Khan, Domlo and Fukhar-ud-din as special cases in Banach spaces. Our results are refinements and generalizations of several recent results from the current literature.

Original language	English
Pages (from-to)	783-791
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	74
Issue number	3
DOIs	https://doi.org/10.1016/j.na.2010.09.029
State	Published - 1 Feb 2011

Keywords

Asymptotically (quasi-)nonexpansive map
CAT(0) space
Common fixed point
Condition (AV)
Convex metric space
Iteration scheme
Semi-compactness

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2010.09.029

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title = "Strong convergence of a general iteration scheme in CAT(0) spaces",

abstract = "We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and CAT(0) spaces. The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step iteration scheme of Xu and Noor and the scheme of Khan, Domlo and Fukhar-ud-din as special cases in Banach spaces. Our results are refinements and generalizations of several recent results from the current literature.",

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T1 - Strong convergence of a general iteration scheme in CAT(0) spaces

AU - Khan, Abdul Rahim

AU - Khamsi, Mohamed Amine

AU - Fukhar-Ud-Din, Hafiz

PY - 2011/2/1

Y1 - 2011/2/1

N2 - We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and CAT(0) spaces. The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step iteration scheme of Xu and Noor and the scheme of Khan, Domlo and Fukhar-ud-din as special cases in Banach spaces. Our results are refinements and generalizations of several recent results from the current literature.

AB - We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and CAT(0) spaces. The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step iteration scheme of Xu and Noor and the scheme of Khan, Domlo and Fukhar-ud-din as special cases in Banach spaces. Our results are refinements and generalizations of several recent results from the current literature.

KW - Asymptotically (quasi-)nonexpansive map

KW - CAT(0) space

KW - Common fixed point

KW - Condition (AV)

KW - Convex metric space

KW - Iteration scheme

KW - Semi-compactness

UR - https://www.scopus.com/pages/publications/78149279929

U2 - 10.1016/j.na.2010.09.029

DO - 10.1016/j.na.2010.09.029

M3 - Article

AN - SCOPUS:78149279929

SN - 0362-546X

VL - 74

SP - 783

EP - 791

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 3

ER -

Strong convergence of a general iteration scheme in CAT(0) spaces

Abstract

Keywords

ASJC Scopus subject areas

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