Common Best Proximity Point Theorems in JS-Metric Spaces Endowed with Graphs

In this paper, we introduce a notion of - proximal edge preserving and dominating - proximal Geraghty for a pair of mappings, which will be used to present some existence and uniqueness results for common best proximity points. Here, the mappings are defined on subsets of a JS-metric space endowed with a directed graph. An example is also provided to support the results. Moreover, we apply our result to a similar setting, where the JS-metric space is endowed with a binary relation.