Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-6822151220241201Fixed point for $\alpha_{*}$-$\psi$-$\beta_{i}$-contractive set-valued mappings on Branciari $S_{b}$-metric space369384849810.22075/ijnaa.2024.28045.3793ENMinoo VataniDepartment of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad
University, Tabriz, IranJalal Hassanzadeh AslDepartment of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran0000-0001-8978-6030Madjid Eshaghi GordjiDepartment of Mathematics, Semnan University, Semnan, IranMohammad Jahangiri RadDepartment of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, IranJournal Article20220811In 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.https://ijnaa.semnan.ac.ir/article_8498_148a81afbd77075455a77b3d2f5d866f.pdf