Certain applications of (α, β)-(ξ, ϖ)-weakly cyclic contractions in C∗-algebra valued G-metric spaces

Abstract

This paper presents a novel class of generalized (α, β)-(ξ, ϖ)-weakly cyclic contraction mappings within the framework of C^∗-algebra valued G-metric spaces (C^∗-AV-G-MS). We establish new common fixed-point theorems that broaden and unify several existing results in the literature. To illustrate the applicability and robustness of our approach, we provide concrete examples. Furthermore, the developed theory is employed to prove the existence and uniqueness of solutions to a functional Equations and to explore implications in homotopy theory.