Common fixed point (\alpha_*-\psi-\beta_{i})-contractive set-valued‎ ‎mappings on orthogonal Branciari S_{b}-metric space

In [۲۴], Khan et al. established some fixed point theorems in complete and compact metric spaces by using altering distance functions. In [۱۶] Gordji et al. described the notion of orthogonal set and orthogonal metric spaces. In [۱۸] Gungor et al. established fixed point theorems on orthogonal metric spaces via altering distance functions. In [۲۵] Lotfy et al introduced the notion of \alpha_{*}-\psi-common rational type mappings on generalized metric spaces with application to fractional integral equations. In [۲۸] 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.

کلیدواژه ها:

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