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

Document Type : Research Paper


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



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.


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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