Approximating common fixed points in hyperbolic spaces

Hafiz Fukhar-Ud-Din; Mohamed Amine Khamsi

doi:10.1186/1687-1812-2014-113

Approximating common fixed points in hyperbolic spaces

Hafiz Fukhar-Ud-Din, Mohamed Amine Khamsi^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

23 Scopus citations

Abstract

We establish strong convergence andδ-convergence theorems of an iteration scheme associated to a pair of nonexpansive mappings on a nonlinear domain. In particular we prove that such a scheme converges to a common fixed point of both mappings. Our results are a generalization of well-known similar results in the linear setting. In particular, we avoid assumptions such as smoothness of the norm, necessary in the linear case.

Original language	English
Article number	113
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2014
DOIs	https://doi.org/10.1186/1687-1812-2014-113
State	Published - May 2014

Keywords

Fixed point
Ishikawa iterations
Nonexpansive mapping
Strong convergence
Uniformly convex hyperbolic space
δ-convergence

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/1687-1812-2014-113

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abstract = "We establish strong convergence andδ-convergence theorems of an iteration scheme associated to a pair of nonexpansive mappings on a nonlinear domain. In particular we prove that such a scheme converges to a common fixed point of both mappings. Our results are a generalization of well-known similar results in the linear setting. In particular, we avoid assumptions such as smoothness of the norm, necessary in the linear case.",

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N2 - We establish strong convergence andδ-convergence theorems of an iteration scheme associated to a pair of nonexpansive mappings on a nonlinear domain. In particular we prove that such a scheme converges to a common fixed point of both mappings. Our results are a generalization of well-known similar results in the linear setting. In particular, we avoid assumptions such as smoothness of the norm, necessary in the linear case.

AB - We establish strong convergence andδ-convergence theorems of an iteration scheme associated to a pair of nonexpansive mappings on a nonlinear domain. In particular we prove that such a scheme converges to a common fixed point of both mappings. Our results are a generalization of well-known similar results in the linear setting. In particular, we avoid assumptions such as smoothness of the norm, necessary in the linear case.

KW - Fixed point

KW - Ishikawa iterations

KW - Nonexpansive mapping

KW - Strong convergence

KW - Uniformly convex hyperbolic space

KW - δ-convergence

UR - https://www.scopus.com/pages/publications/84901794919

U2 - 10.1186/1687-1812-2014-113

DO - 10.1186/1687-1812-2014-113

M3 - Article

AN - SCOPUS:84901794919

SN - 1687-1820

VL - 2014

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

M1 - 113

ER -

Approximating common fixed points in hyperbolic spaces

Abstract

Keywords

ASJC Scopus subject areas

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