Novel Proximal Type Coincidence Point Results with Applications

Abstract

In this paper, the authors establish some intriguing coincidence best proximity point results for proximal contractions in the context of extended b-metric spaces. They give some illustrative examples from various cases to substantiate their conclusions. The findings discussed in the paper are more general, expanding and enhancing a variety of existing findings in the optimal proximity theory. The findings, which explain the proximal coincidence points for multivalued mappings, are the first of their kind in the current state of the art. In addition, the study provides benchmarks for employing the optimal proximity results once the existence and uniqueness requirements are met.

Keywords

Extended b-metric space / Proximal contraction mappings / Coincidence best proximity point / Boundary value problem / Fredholm integral equation / 54E05 / 47H10 / 47H09

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