On externally complete subsets and common fixed points in partially ordered sets

Mohammad Z. Abu-Sbeih; Mohamed A. Khamsi

doi:10.1186/1687-1812-2011-97

On externally complete subsets and common fixed points in partially ordered sets

Mohammad Z. Abu-Sbeih^*
, Mohamed A. Khamsi

^*Corresponding author for this work

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

4 Scopus citations

Abstract

In this study, we introduce the concept of externally complete ordered sets. We discuss the properties of such sets and characterize them in ordered trees. We also prove some common fixed point results for order preserving mappings. In particular, we introduce for the first time the concept of Banach Operator pairs in partially ordered sets and prove a common fixed point result which generalizes the classical De Marr ' s common fixed point theorem.

Original language	English
Article number	97
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2011
DOIs	https://doi.org/10.1186/1687-1812-2011-97
State	Published - Dec 2011

Keywords

Fixed point
Hyperconvex metric spaces
Order preserving mappings
Order trees
Partially ordered sets

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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10.1186/1687-1812-2011-97

Cite this

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abstract = "In this study, we introduce the concept of externally complete ordered sets. We discuss the properties of such sets and characterize them in ordered trees. We also prove some common fixed point results for order preserving mappings. In particular, we introduce for the first time the concept of Banach Operator pairs in partially ordered sets and prove a common fixed point result which generalizes the classical De Marr ' s common fixed point theorem.",

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AB - In this study, we introduce the concept of externally complete ordered sets. We discuss the properties of such sets and characterize them in ordered trees. We also prove some common fixed point results for order preserving mappings. In particular, we introduce for the first time the concept of Banach Operator pairs in partially ordered sets and prove a common fixed point result which generalizes the classical De Marr ' s common fixed point theorem.

KW - Fixed point

KW - Hyperconvex metric spaces

KW - Order preserving mappings

KW - Order trees

KW - Partially ordered sets

UR - https://www.scopus.com/pages/publications/84884244655

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DO - 10.1186/1687-1812-2011-97

M3 - Article

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JO - Fixed Point Theory and Algorithms for Sciences and Engineering

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M1 - 97

ER -

On externally complete subsets and common fixed points in partially ordered sets

Abstract

Keywords

ASJC Scopus subject areas

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