Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces ℓp(·)

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequen...

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Main Authors:	Afrah A. N. Abdou, Mohamed Amine Khamsi
Format:	Article
Language:	English
Published:	MDPI AG 2020-01-01
Series:	Mathematics
Subjects:	electrorheological fluids fixed point kannan contraction mapping kannan nonexpansive mapping modular vector spaces nakano
Online Access:	https://www.mdpi.com/2227-7390/8/1/76

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spelling	doaj-1b0edccbf42a427793bbab67cc9cdafa2020-11-25T02:05:54ZengMDPI AGMathematics2227-73902020-01-01817610.3390/math8010076math8010076Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub>Afrah A. N. Abdou0Mohamed Amine Khamsi1Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USAKannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces <inline-formula> <math display="inline"> <semantics> <msub> <mo>ℓ</mo> <mrow> <mi>p</mi> <mo>(</mo> <mo>·</mo> <mo>)</mo> </mrow> </msub> </semantics> </math> </inline-formula>. We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before.https://www.mdpi.com/2227-7390/8/1/76electrorheological fluidsfixed pointkannan contraction mappingkannan nonexpansive mappingmodular vector spacesnakano
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Afrah A. N. Abdou Mohamed Amine Khamsi
spellingShingle	Afrah A. N. Abdou Mohamed Amine Khamsi Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub> Mathematics electrorheological fluids fixed point kannan contraction mapping kannan nonexpansive mapping modular vector spaces nakano
author_facet	Afrah A. N. Abdou Mohamed Amine Khamsi
author_sort	Afrah A. N. Abdou
title	Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub>
title_short	Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub>
title_full	Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub>
title_fullStr	Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub>
title_full_unstemmed	Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub>
title_sort	fixed points of kannan maps in the variable exponent sequence spaces <i>ℓ</i><sub><i>p</i>(·)</sub>
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-01-01
description	Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces <inline-formula> <math display="inline"> <semantics> <msub> <mo>ℓ</mo> <mrow> <mi>p</mi> <mo>(</mo> <mo>·</mo> <mo>)</mo> </mrow> </msub> </semantics> </math> </inline-formula>. We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before.
topic	electrorheological fluids fixed point kannan contraction mapping kannan nonexpansive mapping modular vector spaces nakano
url	https://www.mdpi.com/2227-7390/8/1/76
work_keys_str_mv	AT afrahanabdou fixedpointsofkannanmapsinthevariableexponentsequencespacesilisubipisub AT mohamedaminekhamsi fixedpointsofkannanmapsinthevariableexponentsequencespacesilisubipisub
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Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces <i>ℓ</i><sub><i>p</i>(·)</sub>

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