A Study on Common Fixed Point of Joint A;B Generalized Cyclic ϕ−abc Weak Nonexpansive Mappings and Generalized Cyclic abc;r Contractions in Quasi Metric Spaces

Abstract

This manuscript proves the existence of a single common fixed point of two joint A,B generalized cyclic ϕ−abc weak nonexpansive mappings, where A and B are compact sets. The result in particular demonstrated a single fixed point of generalized cyclic ϕ−abc weak nonexpansive mappings, without the assumption of a single contracting point. Additionally, it introduces new types of generalized cyclic abc;r contraction mappings and describes the existence of a single fixed point of them in b-metric spaces. Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic abc;r contraction mappings, extend, and generalize some of the previous reported results.