On $T_\beta$-contractive mappings: Fixed point results with an application

Document Type : Research Paper

Authors

Equipe de Recherche en Mathematiques Appliquees, Technologies de l'Information et de la Communication Faculte Polydisciplinare de Khouribga, Universite Sultan Moulay Slimane de Beni-Mellal, Morocco

Abstract

We introduce the concept of $T_\beta$-contractive mappings in the framework of bounded metric spaces and prove the existence of a fixed point for such mappings without using neither the compactness nor the uniform convexity of the space. Furthermore, a fixed point theorem for $T_{\beta}$-weakly contractive maps has been given. We point out that, these results generalize and improve many previous works in the literature.    Ultimately, one of our theoretical results has been implicated to study the existence of the solution to a class of functional equations arising in dynamic programming under new weak conditions.

Keywords

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Volume 13, Issue 2
July 2022
Pages 2771-2779
  • Receive Date: 23 February 2022
  • Revise Date: 29 May 2022
  • Accept Date: 25 June 2022