Convergence of a general algorithm of asymptotically nonexpansive maps in uniformly convex hyperbolic spaces

A. R. Khan; H. Fukhar-Ud-Din; A. Kalsoom; B. S. Lee

doi:10.1016/j.amc.2014.04.005

Convergence of a general algorithm of asymptotically nonexpansive maps in uniformly convex hyperbolic spaces

A. R. Khan
, H. Fukhar-Ud-Din
, A. Kalsoom
, B. S. Lee^*

^*Corresponding author for this work

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

6 Scopus citations

Abstract

In this paper, we establish convergence theorems for a general algorithm of an asymptotically nonexpansive map in a uniformly convex hyperbolic space. Our results generalize simultaneously the approximation results of Rhoades (1994) [18], Suantai (2005) [20] and Xu and Noor (2002) [26] on a nonlinear domain. Our results are refinements and generalizations of the corresponding ones in uniformly convex Banach spaces and CAT(0) spaces.

Original language	English
Pages (from-to)	547-556
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	238
DOIs	https://doi.org/10.1016/j.amc.2014.04.005
State	Published - 1 Jul 2014

Bibliographical note

Funding Information:
A.R. Khan and H. Fukhar-ud-din are grateful to King Fahd University of Petroleum & Minerals for supporting research project IN 121037. Amna Kalsoom gratefully acknowledges Higher Education Commission (HEC) of Pakistan for financial support during this research.

Keywords

Asymptotically nonexpansive map
General algorithm
Uniformly convex metric space
Δ - Convergence and strong convergence

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2014.04.005

Cite this

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title = "Convergence of a general algorithm of asymptotically nonexpansive maps in uniformly convex hyperbolic spaces",

abstract = "In this paper, we establish convergence theorems for a general algorithm of an asymptotically nonexpansive map in a uniformly convex hyperbolic space. Our results generalize simultaneously the approximation results of Rhoades (1994) [18], Suantai (2005) [20] and Xu and Noor (2002) [26] on a nonlinear domain. Our results are refinements and generalizations of the corresponding ones in uniformly convex Banach spaces and CAT(0) spaces.",

keywords = "Asymptotically nonexpansive map, General algorithm, Uniformly convex metric space, Δ - Convergence and strong convergence",

author = "Khan, \{A. R.\} and H. Fukhar-Ud-Din and A. Kalsoom and Lee, \{B. S.\}",

note = "Funding Information: A.R. Khan and H. Fukhar-ud-din are grateful to King Fahd University of Petroleum \& Minerals for supporting research project IN 121037. Amna Kalsoom gratefully acknowledges Higher Education Commission (HEC) of Pakistan for financial support during this research.",

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AU - Khan, A. R.

AU - Fukhar-Ud-Din, H.

AU - Kalsoom, A.

AU - Lee, B. S.

N1 - Funding Information: A.R. Khan and H. Fukhar-ud-din are grateful to King Fahd University of Petroleum & Minerals for supporting research project IN 121037. Amna Kalsoom gratefully acknowledges Higher Education Commission (HEC) of Pakistan for financial support during this research.

PY - 2014/7/1

Y1 - 2014/7/1

N2 - In this paper, we establish convergence theorems for a general algorithm of an asymptotically nonexpansive map in a uniformly convex hyperbolic space. Our results generalize simultaneously the approximation results of Rhoades (1994) [18], Suantai (2005) [20] and Xu and Noor (2002) [26] on a nonlinear domain. Our results are refinements and generalizations of the corresponding ones in uniformly convex Banach spaces and CAT(0) spaces.

AB - In this paper, we establish convergence theorems for a general algorithm of an asymptotically nonexpansive map in a uniformly convex hyperbolic space. Our results generalize simultaneously the approximation results of Rhoades (1994) [18], Suantai (2005) [20] and Xu and Noor (2002) [26] on a nonlinear domain. Our results are refinements and generalizations of the corresponding ones in uniformly convex Banach spaces and CAT(0) spaces.

KW - Asymptotically nonexpansive map

KW - General algorithm

KW - Uniformly convex metric space

KW - Δ - Convergence and strong convergence

UR - https://www.scopus.com/pages/publications/84901009021

U2 - 10.1016/j.amc.2014.04.005

DO - 10.1016/j.amc.2014.04.005

M3 - Article

AN - SCOPUS:84901009021

SN - 0096-3003

VL - 238

SP - 547

EP - 556

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Convergence of a general algorithm of asymptotically nonexpansive maps in uniformly convex hyperbolic spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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