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

Author

Listed:
  • Afrah A. N. Abdou

    (Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, University of Jeddah, Jeddah 23218, Saudi Arabia)

  • Mohamed Amine Khamsi

    (Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA)

Abstract

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 ℓ 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.

Suggested Citation

  • Afrah A. N. Abdou & Mohamed Amine Khamsi, 2020. "Fixed Points of Kannan Maps in the Variable Exponent Sequence Spaces ℓ p (·)," Mathematics, MDPI, vol. 8(1), pages 1-7, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:76-:d:304742
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    References listed on IDEAS

    as
    1. M. Bachar & M. A. Khamsi & O. Mendez & M. Bounkhel, 2019. "A geometric property in ℓp(·) and its applications," Mathematische Nachrichten, Wiley Blackwell, vol. 292(9), pages 1931-1940, September.
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