On Fixed Point Results for Hybrid-Interpolative Reich-Istratescu-Type Contractions within the Framework of Soft Metric Spaces

Abstract

In this study, we extend the class of hybrid-interpolative Reich-Istratescu-type contractions, recently introduced by Karapınar et al. (2022), to the framework of soft metric spaces-a generalized structure that integrates soft set theory with classical metric spaces to model uncertainty. We rigorously define these contractions within soft metric spaces, leveraging the concepts of soft points and soft mappings. A series of fixed point theorems are established under these generalized contractive conditions, demonstrating the existence and uniqueness of fixed points. Novel analytical techniques are employed to validate the theoretical results, and illustrative examples further highlight their practical applicability. These findings advance fixed point theory in soft metric spaces and offer new perspectives for applications in optimization, control theory, and computational mathematics where uncertainty is inherent.