Some Novel Proximal Point Results and Applications

The current study provides significant findings on coincidence the best proximity points for proximal-contractions in the context of extended $b$-metric spaces. To substantiate our assertions, we present illustrative examples across several circumstances. The conclusions presented in this study provide an expanded and more nuanced viewpoint, extending and generalizing multiple previous findings in optimal proximity theory. These findings present a new method for comprehending proximal coincidence locations in multi-valued mappings, representing a substantial advancement in the existing research landscape. This work gives practical benchmarks for implementing optimal proximity results, provided that existence and uniqueness constraints are met.