Fixed point results of pointwise contractions in modular metric spaces

Afrah A.N. Abdou; Mohamed A. Khamsi

doi:10.1186/1687-1812-2013-163

Fixed point results of pointwise contractions in modular metric spaces

Afrah A.N. Abdou^*
, Mohamed A. Khamsi

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

31 Scopus citations

Abstract

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate the existence of fixed points of modular contractive mappings in modular metric spaces. These are related to the successive approximations of fixed points (via orbits) which converge to the fixed points in the modular sense, which is weaker than the metric convergence.

Original language	English
Article number	163
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2013
DOIs	https://doi.org/10.1186/1687-1812-2013-163
State	Published - Jun 2013

Keywords

Fixed point
Modular function space
Modular metric spaces
Orlicz spaces
Pointwise contraction mapping

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/1687-1812-2013-163

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abstract = "The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate the existence of fixed points of modular contractive mappings in modular metric spaces. These are related to the successive approximations of fixed points (via orbits) which converge to the fixed points in the modular sense, which is weaker than the metric convergence.",

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AB - The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate the existence of fixed points of modular contractive mappings in modular metric spaces. These are related to the successive approximations of fixed points (via orbits) which converge to the fixed points in the modular sense, which is weaker than the metric convergence.

KW - Fixed point

KW - Modular function space

KW - Modular metric spaces

KW - Orlicz spaces

KW - Pointwise contraction mapping

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ER -

Fixed point results of pointwise contractions in modular metric spaces

Abstract

Keywords

ASJC Scopus subject areas

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