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

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Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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Department of Mathematics, Faculty of Sciences, Jeddah University, Jeddah 23218, Saudi Arabia
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Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 76; https://doi.org/10.3390/math8010076
Received: 5 December 2019 / Revised: 25 December 2019 / Accepted: 26 December 2019 / Published: 3 January 2020
(This article belongs to the Special Issue New Trends in Analysis and Geometry)
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 p ( · ) . 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. View Full-Text
Keywords: electrorheological fluids; fixed point; Kannan contraction mapping; Kannan nonexpansive mapping; modular vector spaces; Nakano electrorheological fluids; fixed point; Kannan contraction mapping; Kannan nonexpansive mapping; modular vector spaces; Nakano
MDPI and ACS Style

Abdou, A.A.N.; Khamsi, M.A. Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces p(·). Mathematics 2020, 8, 76.

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