Abstract
Abstract In this article, an application of φ-metric is given via a geometrical example to show how it can help to measure distance for non-planar surfaces where the classical metric becomes incapable. We also introduce the concept of best proximity point and proximal contraction for a class of mappings in a φ-metric space and prove a best proximity point theorem for such class of contraction mappings from which the famous “Wardowski’s fixed point theorem” can be deduced as a particular case. To support our theorem, we provide an example in which Wardowski’s metric fixed point theorem cannot be applied.
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