Abstract

A best proximity point for a non-selfmapping is that point whose distance from its image is as small as possible. In mathematical language, if X is any space, A and B are two subsets of X and T: A → B is a mapping. We can say that x is best proximity point if d(x, Tx) = d(A, B) and this best proximity point reduces to fixed point if mapping T is a selfmapping. The main objective in this paper is to prove the best proximity point theorem for the notion of Geraghty-contractions by using MT-function β which satisfies Mizoguchi-Takahashi’s condition (equation (i)) in the context of metric space and we also provide an example to support our main result.

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