Analysis of Best Proximity Points in F-Metric Spaces with Applications

The primary objective of this study is to introduce the concept of α-interpolative proximal contractions within the framework of F-metric spaces and to derive corresponding best proximity point results for these newly defined contractions. As a direct implication of the main theorems, best proximity results for single-valued mappings are also established. Moreover, we extend our investigation to partially ordered F-metric spaces, examining how graph structures influence best proximity point theory in this context. In addition, several fixed point theorems are obtained as immediate consequences of the proposed results. To illustrate the validity of our theoretical developments, non-trivial examples are provided.