An application of $\phi$-metric and related best proximity point results generalizing Wardowski's fixed point theorem

Abhishikta Das, Sumit Som, Hemanta Kalita, Tarapada Bag

Abstract


In this article, an application of $\phi$-metric is given via geometrical example
to show how it can help to measure distance for non-planer surfaces
where the classical metric become incapable. Also, we introduce the concept
of best proximity point and proximal contraction
for a class of mappings
in a $\phi$-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. We provide an example in support
of our theorem
in which the Wardowski's metric fixed point theorem can not be applied.

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DOI: https://doi.org/10.2478/tmmp-2024-0011