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In this paper, we introduce a notion of  G -proximal edge preserving and dominating  G -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.

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