Some fixed-point theorems of convex orbital $(\alpha, \beta )$-contraction mappings in geodesic spaces

Abstract The aim of this paper is to broaden the applicability convex orbital $(\alpha, \beta )$ ( α , β ) -contraction mappings geodesic spaces. This class a natural extension iterated contraction mappings. derives fixed-point theorems both with and without assuming continuity. Furthermore, investigates monotone establishes theorem for