Best proximity points of contractive mappings on a metric space with a graph and applications

Asrifa Sultana, V. Vetrivel


We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent  fixed point and best proximity point results.


Fixed point; best proximity point; contraction; graph; metric space; P-property.

Subject classification

54H25; 47H10.

Full Text:



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