Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 14 12 2023 12 01 Common fixed point ($\alpha_*$-$\psi$-$\beta_{i}$)-contractive set-valued‎ ‎mappings on orthogonal Branciari $S_{b}$-metric space 105 120 7452 10.22075/ijnaa.2023.27426.3597 EN Mohammad Rashea Shaeri Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran Jalal Hassanzadeh Asl Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran Madjid Eshaghi Gordji Department of Mathematics, Semnan University, Semnan, Iran Hassan Refaghat Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran Journal Article 2022 06 08 In [24], Khan et al. established some fixed point theorems in complete and compact metric spaces by using altering distance functions. In [16] Gordji et al. described the notion of orthogonal set and orthogonal metric spaces. In [18] Gungor et al. established fixed point theorems on orthogonal metric spaces via altering distance functions. In [25] Lotfy et al introduced the notion of $\alpha_{*}$-$\psi$-common rational type mappings on generalized metric spaces with application to fractional integral equations. In [28] K. Royy 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 the common fixed point ($\alpha_*$-$\psi$-$\beta_{i}$)-contractive set-valued mappings on orthogonal Branciari $S_{b}$-metric space with the application of the existence of a unique solution to an initial value problem. https://ijnaa.semnan.ac.ir/article_7452_71cc107d2e0408e60a3d3c44f47507bd.pdf