On common fixed points in modular vector spaces

Afrah A.N. Abdou; Mohamed A. Khamsi

doi:10.1186/s13663-015-0478-z

On common fixed points in modular vector spaces

Afrah A.N. Abdou, Mohamed A. Khamsi

Mathematics

King Abdulaziz University

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

6 Scopus citations

Abstract

In this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr’s common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces.

Original language	British English
Article number	229
Pages (from-to)	1-9
Number of pages	9
Journal	Fixed Point Theory and Applications
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13663-015-0478-z
State	Published - 1 Dec 2015

Keywords

Banach operator pair
electrorheological fluids
fixed point
KKM-mapping
modular function space
modular metric space
retraction

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10.1186/s13663-015-0478-z

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title = "On common fixed points in modular vector spaces",

abstract = "In this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr{\textquoteright}s common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces.",

keywords = "Banach operator pair, electrorheological fluids, fixed point, KKM-mapping, modular function space, modular metric space, retraction",

author = "Abdou, {Afrah A.N.} and Khamsi, {Mohamed A.}",

note = "Funding Information: This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. 372-501-D1435. The authors, therefore, gratefully acknowledge the DSR technical and financial support. Publisher Copyright: {\textcopyright} 2015, Abdou and Khamsi.",

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AU - Khamsi, Mohamed A.

N1 - Funding Information: This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. 372-501-D1435. The authors, therefore, gratefully acknowledge the DSR technical and financial support. Publisher Copyright: © 2015, Abdou and Khamsi.

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N2 - In this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr’s common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces.

AB - In this work, we discuss the concept of Banach operator pairs in modular vector spaces. We prove the existence of common fixed points for these type of operators which satisfy a modular continuity in modular compact sets. On the basis of our result, we are able to give an analog of DeMarr’s common fixed point theorem for a family of symmetric Banach operator pairs in modular vector spaces.

KW - Banach operator pair

KW - electrorheological fluids

KW - fixed point

KW - KKM-mapping

KW - modular function space

KW - modular metric space

KW - retraction

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SN - 1687-1820

VL - 2015

SP - 1

EP - 9

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

IS - 1

M1 - 229

ER -

On common fixed points in modular vector spaces

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