Abstract

In this paper we introduce a notion of $\alpha$-Greaghty contraction type maps in the setting of a metric space. We also establish a Best Proximity point theorem for such maps using $p$-property.

Keywords and Phrases

Best Proximity point, $\alpha$-Geraghty contraction type map, metric spaces, $p$-property, triangular $\alpha$-admissible, generalized $\alpha$-Geraghty contraction.

A.M.S. subject classification

47H10.

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