Weak Commuting Mappings and its Variants for Generalized ψ- Weak Contraction in Perturbed Metric Spaces

Abstract

In this paper, we establish several common fixed-point theorems in the setting of perturbed metric spaces, where the usual distance is replaced by the perturbed distance

with representing a non-negative perturbation kernel. Working in this generalized framework, we investigate weakly commuting mappings and their pointwise extensions, including -weakly commuting and reciprocally continuous mappings. Further, we study -weakly commuting mappings of type (P) under a generalized -weak contraction condition formulated with cubic and quadratic powers of the perturbed distance . These results significantly extend the classical metric-space theorems to situations involving measurement errors and structural perturbations.