Variants of Compatible Mappings and Fixed Point Results in Perturbed Metric Spaces

Résumé

In this paper, we introduce variants of compatible mappings namely compatible mappings of types (K), (R) and (E) along with the concept of faintly compatible mappings in the setting of perturbed metric spaces. These classes extend and generalize the existing notions of compatible and weakly compatible mappings. For each of these classes, we establish common fixed point theorems for four self-mappings satisfying contraction-type conditions. The results obtained unify and extend several well-known fixed point results in the literature, providing a broader framework for the study of fixed points in perturbed metric spaces. Illustrative examples are included to demonstrate the applicability of the proved theorems.