Fixed point results for a generalized nonexpansive map in uniformly convex metric spaces

H. Fukhar-Ud-Din; A. R. Khan; Z. Akhtar

doi:10.1016/j.na.2012.03.025

Fixed point results for a generalized nonexpansive map in uniformly convex metric spaces

H. Fukhar-Ud-Din
, A. R. Khan^*
, Z. Akhtar

^*Corresponding author for this work

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

26 Scopus citations

Abstract

In this paper, the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved. This fixed point is approximated by averaging Krasnosel'skii iterations of a generalized nonexpansive map. Our results substantially improve and extend several known results existing in the literature.

Original language	English
Pages (from-to)	4747-4760
Number of pages	14
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	75
Issue number	13
DOIs	https://doi.org/10.1016/j.na.2012.03.025
State	Published - Sep 2012

Keywords

Averaging Krasnosel'skii iterations
Convex metric space
Fixed point
Generalized nonexpansive map
Strong convergence

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2012.03.025

Cite this

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abstract = "In this paper, the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved. This fixed point is approximated by averaging Krasnosel'skii iterations of a generalized nonexpansive map. Our results substantially improve and extend several known results existing in the literature.",

keywords = "Averaging Krasnosel'skii iterations, Convex metric space, Fixed point, Generalized nonexpansive map, Strong convergence",

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AU - Khan, A. R.

AU - Akhtar, Z.

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AB - In this paper, the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved. This fixed point is approximated by averaging Krasnosel'skii iterations of a generalized nonexpansive map. Our results substantially improve and extend several known results existing in the literature.

KW - Averaging Krasnosel'skii iterations

KW - Convex metric space

KW - Fixed point

KW - Generalized nonexpansive map

KW - Strong convergence

UR - https://www.scopus.com/pages/publications/84862138833

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DO - 10.1016/j.na.2012.03.025

M3 - Article

AN - SCOPUS:84862138833

SN - 0362-546X

VL - 75

SP - 4747

EP - 4760

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 13

ER -

Fixed point results for a generalized nonexpansive map in uniformly convex metric spaces

Abstract

Keywords

ASJC Scopus subject areas

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