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

Abstract

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