Common fixed point and invariant approximation in hyperbolic ordered metric spaces

Mujahid Abbas; Mohamed Amine Khamsi; Abdul Rahim Khan

doi:10.1186/1687-1812-2011-25

Common fixed point and invariant approximation in hyperbolic ordered metric spaces

Mujahid Abbas
, Mohamed Amine Khamsi
, Abdul Rahim Khan^*

^*Corresponding author for this work

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

23 Scopus citations

Abstract

We prove a common fixed point theorem for four mappings defined on an ordered metric space and apply it to find new common fixed point results. The existence of common fixed points is established for two or three noncommuting mappings where T is either ordered S-contraction or ordered asymptotically S-nonexpansive on a nonempty ordered starshaped subset of a hyperbolic ordered metric space. As applications, related invariant approximation results are derived. Our results unify, generalize, and complement various known comparable results from the current literature.

Original language	English
Article number	25
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2011
DOIs	https://doi.org/10.1186/1687-1812-2011-25
State	Published - Aug 2011

Keywords

Best approximation
Common fixed point
Hyperbolic metric space
Ordered asymptotically S-nonexpansive mapping

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/1687-1812-2011-25

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title = "Common fixed point and invariant approximation in hyperbolic ordered metric spaces",

abstract = "We prove a common fixed point theorem for four mappings defined on an ordered metric space and apply it to find new common fixed point results. The existence of common fixed points is established for two or three noncommuting mappings where T is either ordered S-contraction or ordered asymptotically S-nonexpansive on a nonempty ordered starshaped subset of a hyperbolic ordered metric space. As applications, related invariant approximation results are derived. Our results unify, generalize, and complement various known comparable results from the current literature.",

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AU - Khamsi, Mohamed Amine

AU - Khan, Abdul Rahim

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N2 - We prove a common fixed point theorem for four mappings defined on an ordered metric space and apply it to find new common fixed point results. The existence of common fixed points is established for two or three noncommuting mappings where T is either ordered S-contraction or ordered asymptotically S-nonexpansive on a nonempty ordered starshaped subset of a hyperbolic ordered metric space. As applications, related invariant approximation results are derived. Our results unify, generalize, and complement various known comparable results from the current literature.

AB - We prove a common fixed point theorem for four mappings defined on an ordered metric space and apply it to find new common fixed point results. The existence of common fixed points is established for two or three noncommuting mappings where T is either ordered S-contraction or ordered asymptotically S-nonexpansive on a nonempty ordered starshaped subset of a hyperbolic ordered metric space. As applications, related invariant approximation results are derived. Our results unify, generalize, and complement various known comparable results from the current literature.

KW - Best approximation

KW - Common fixed point

KW - Hyperbolic metric space

KW - Ordered asymptotically S-nonexpansive mapping

UR - https://www.scopus.com/pages/publications/84898922349

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DO - 10.1186/1687-1812-2011-25

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M1 - 25

ER -

Common fixed point and invariant approximation in hyperbolic ordered metric spaces

Abstract

Keywords

ASJC Scopus subject areas

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