This paper is aimed at studying the uniqueness of coincidence best proximity point for -proximal contractions in complete Branciari metric space. Throughout this article, discontinuity of the Branciari metric space is used and we obtained the desired results without assuming it as a continuous. Some examples are provided to validate the results proved herein. As an application, we derive the best proximity point results in the setup of complete Branciari metric space endowed with graph. Further, our results extend and generalize the existing ones in literature.

中文翻译：

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Branciari度量空间中的重合最佳接近点结果及其应用

本文旨在研究重合的最佳邻近点的唯一性。 -完整的Branciari度量空间中的近端收缩。在整个本文中，使用了Branciari度量空间的不连续性，我们获得了预期的结果，而没有假定它是连续的。提供了一些示例来验证此处证明的结果。作为应用程序，我们在设置图的完整Branciari度量空间的过程中获得了最佳的邻近点结果。此外，我们的结果扩展并概括了文献中的现有文献。