Reimagining Fixed Points: Exploring the Role of Occasionally Weakly Compatible Mappings in Fuzzy Metrics

Abstract

In this work, we revisit the concept of fixed points by exploring the role of occasionally weakly compatible (OWC) mappings within the structure of fuzzy metric spaces. Building on the classical fixed point theory, we investigate new conditions under which tripled fixed points exist and are unique. By employing the framework of fuzzy metrics and leveraging the flexibility of OWC mappings, we establish a generalized tripled fixed point theorem that extends several known results. We also explore the concept of tripled fixed points for occasionally weakly compatible mappings within the framework of fuzzy metric spaces. We establish several novel tripled fixed-point theorems that extend existing results in this area. Additionally, to validate the applicability of our theorems, we provide detailed illustrative examples that demonstrate the effectiveness and relevance of the established results in fuzzy metric settings. These findings contribute to the broader understanding of fixed-point theory in fuzzy environments and open new avenues for future research in generalized metric spaces and their applications.