Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces

Abdul Rahim Khan; Abdul Aziz Domlo; Hafiz Fukhar-ud-din

doi:10.1016/j.jmaa.2007.06.051

Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces

Abdul Rahim Khan^*
, Abdul Aziz Domlo
, Hafiz Fukhar-ud-din

^*Corresponding author for this work

Department of Mathematics

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

52 Scopus citations

Abstract

In this paper, we introduce a general iteration scheme for a finite family of asymptotically quasi-nonexpansive mappings. The new iterative scheme includes the modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor and Khan and Takahashi scheme as special cases. Our results are generalizations as well as refinement of several known results in the current literature.

Original language	English
Pages (from-to)	1-11
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	341
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2007.06.051
State	Published - 1 May 2008

Bibliographical note

Funding Information:
The authors thank the referee for useful suggestions to improve presentation of the paper. The author A.R. Khan gratefully acknowledges support provided by King Fahd University of Petroleum and Minerals during this research.

Keywords

Asymptotically quasi-nonexpansive mapping
Banach space
Common fixed point
Modified Mann and Ishikawa iterations
Weak and strong convergence

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2007.06.051

Cite this

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title = "Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces",

abstract = "In this paper, we introduce a general iteration scheme for a finite family of asymptotically quasi-nonexpansive mappings. The new iterative scheme includes the modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor and Khan and Takahashi scheme as special cases. Our results are generalizations as well as refinement of several known results in the current literature.",

keywords = "Asymptotically quasi-nonexpansive mapping, Banach space, Common fixed point, Modified Mann and Ishikawa iterations, Weak and strong convergence",

author = "Khan, \{Abdul Rahim\} and Domlo, \{Abdul Aziz\} and Hafiz Fukhar-ud-din",

note = "Funding Information: The authors thank the referee for useful suggestions to improve presentation of the paper. The author A.R. Khan gratefully acknowledges support provided by King Fahd University of Petroleum and Minerals during this research.",

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AU - Khan, Abdul Rahim

AU - Domlo, Abdul Aziz

AU - Fukhar-ud-din, Hafiz

N1 - Funding Information: The authors thank the referee for useful suggestions to improve presentation of the paper. The author A.R. Khan gratefully acknowledges support provided by King Fahd University of Petroleum and Minerals during this research.

PY - 2008/5/1

Y1 - 2008/5/1

N2 - In this paper, we introduce a general iteration scheme for a finite family of asymptotically quasi-nonexpansive mappings. The new iterative scheme includes the modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor and Khan and Takahashi scheme as special cases. Our results are generalizations as well as refinement of several known results in the current literature.

AB - In this paper, we introduce a general iteration scheme for a finite family of asymptotically quasi-nonexpansive mappings. The new iterative scheme includes the modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor and Khan and Takahashi scheme as special cases. Our results are generalizations as well as refinement of several known results in the current literature.

KW - Asymptotically quasi-nonexpansive mapping

KW - Banach space

KW - Common fixed point

KW - Modified Mann and Ishikawa iterations

KW - Weak and strong convergence

UR - https://www.scopus.com/pages/publications/38849204295

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JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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