Existence and higher arity iteration for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

Muhammad Aqeel Ahmad Khan; Hafiz Fukhar-ud-din; Amna Kalsoom

doi:10.1186/s13663-015-0483-2

Existence and higher arity iteration for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

Muhammad Aqeel Ahmad Khan^*, Hafiz Fukhar-ud-din, Amna Kalsoom

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

10 Scopus citations

Abstract

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu (J. Math. Anal. Appl. 333:128-141, 2007) in such a setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and △-convergence results which extend and generalize various corresponding results established in the current literature.

Original language	English
Article number	3
Pages (from-to)	1-18
Number of pages	18
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1186/s13663-015-0483-2
State	Published - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© 2016, Khan et al.

Keywords

asymptotic center
common fixed point
hyperbolic space
modulus of uniform convexity
total asymptotically nonexpansive mapping

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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Cite this

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abstract = "This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu (J. Math. Anal. Appl. 333:128-141, 2007) in such a setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and △-convergence results which extend and generalize various corresponding results established in the current literature.",

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AU - Fukhar-ud-din, Hafiz

AU - Kalsoom, Amna

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N2 - This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu (J. Math. Anal. Appl. 333:128-141, 2007) in such a setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and △-convergence results which extend and generalize various corresponding results established in the current literature.

AB - This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu (J. Math. Anal. Appl. 333:128-141, 2007) in such a setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and △-convergence results which extend and generalize various corresponding results established in the current literature.

KW - asymptotic center

KW - common fixed point

KW - hyperbolic space

KW - modulus of uniform convexity

KW - total asymptotically nonexpansive mapping

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IS - 1

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ER -

Existence and higher arity iteration for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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