Fixed point for $\alpha_{*}$-$\psi$-$\beta_{i}$-contractive set-valued mappings on Branciari $S_{b}$-metric space

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Faculty of Science‎, ‎Tabriz Branch‎, ‎Islamic Azad‎ ‎‎‎University‎, ‎Tabriz‎, ‎Iran

2 Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran

3 Department of Mathematics, Semnan University, Semnan, Iran

10.22075/ijnaa.2024.28045.3793

Abstract

In 1984, Khan et al. established some fixed point theorems in complete and compact metric spaces by altering distance functions. In 2020, Lotfy et al. introduced the $\alpha_{*}$-$\psi$-common rational type mappings on generalized metric spaces applied to fractional integral equations. In 2022, Roy et al. described the notion of Branciari  $ S_b$-metric space and related fixed point theorems with an application. In this paper, we introduce the notion of fixed point theorems for $\alpha_{*}$-$\psi$-$\beta_{i}$-contractive set-valued mappings on Branciari $S_{b}$-metric space with application to fractional integral equations.

Keywords

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Articles in Press, Corrected Proof
Available Online from 08 February 2024
  • Receive Date: 11 August 2022
  • Revise Date: 15 January 2024
  • Accept Date: 01 February 2024