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 ðA, BÞ 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.