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 $\left(A,B\right)$ generalized cyclic $\varphi -abc$ weak nonexpansive mappings, where $A$ and $B$ are compact sets. The result in particular demonstrated a single fixed point of generalized cyclic $\varphi -abc$ 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.