An application of $\phi$-metric and related best proximity point results generalizing Wardowski's fixed point theorem
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.
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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Subscribers OnlyDOI: https://doi.org/10.2478/tmmp-2024-0011