common fixed point (α∗-ψ-βi)-contractive set-valued mappings on orthogonal branciari sb-metric space

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 α∗-ψ-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 sb-metric space and related fixed point theorems with an application. in this paper, we introduce the notion of the common fixed point (α∗-ψ-βi)-contractive set-valued mappings on orthogonal branciari sb-metric space with the application of the existence of a unique solution to an initial value problem.