Best Proximity Point Theorems for G,D-Proximal Geraghty Maps in JS-Metric Spaces

We study G,D-proximal Geraghty contractions in a JS-metric space X endowed with graph G. We obtain some best proximity theorems for such contractions. An example and several consequences are given. As a consequence of our results, we also provide the best proximity point results in X endowed with a binary relation

Best Proximity Coincidence Point Results for α,D-Proximal Generalized Geraghty Mappings in JS-Metric Spaces

We introduce a type of Geraghty contractions in a JS-metric space X, called α,D-proximal generalized Geraghty mappings. By using the triangular-α,D-proximal admissible property, we obtain the existence and uniqueness theorem of best proximity coincidence points for these mappings together with some corollaries and illustrative examples. As an application, we give a best proximity coincidence point result in X endowed with a binary relation

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

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