Document Type : Research Paper

Authors

• Mohammad Rashea Shaeri ¹
• Jalal Hassanzadeh Asl ¹
• Madjid Eshaghi Gordji ²
• Hassan Refaghat ¹

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

² Department of Mathematics, Semnan University, Semnan, Iran

Abstract

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.

Keywords

• $\alpha_*$-$\psi$-$\beta_{i}$)-contractive
• Branciari $S_{b}$-metric space
• Common fixed point
• ‎ ‎Solution to an initial value problem