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

Abstract

Abstract The aim of this paper is to broaden the applicability of convex orbital ( α , β ) $(\alpha, \beta )$ -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 ( α , β ) $(\alpha, \beta )$ -contraction mappings and establishes a fixed-point theorem for this class of mappings.

Keywords

• Iterated contraction
• Geodesic space
• Partial order