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Common α -Fuzzy Fixed Point Results for F -Contractions with Applications

Author

Listed:
  • Jamshaid Ahmad

    (Department of Mathematics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia)

  • Giuseppe Marino

    (Department of Mathematics and Computer Science, University of Calabria, Via P. Bucci, 87036 Arcavacata di Rende (CS), Italy)

  • Saleh Abdullah Al-Mezel

    (Department of Mathematics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia)

Abstract

F -contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α -fuzzy mappings in b -metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α -fuzzy fixed point results for F -contractions in b -metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature.

Suggested Citation

  • Jamshaid Ahmad & Giuseppe Marino & Saleh Abdullah Al-Mezel, 2021. "Common α -Fuzzy Fixed Point Results for F -Contractions with Applications," Mathematics, MDPI, vol. 9(3), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:277-:d:490092
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