<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article, an application of <italic>φ</italic>-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 <italic>φ</italic>-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.</p>
</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.

An Application of <italic>φ</italic>-Metric and Related Best Proximity Point Results Generalizing Wardowski’s Fixed Point Theorem

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

An Application of -Metric and Related Best Proximity Point Results Generalizing Wardowski’s Fixed Point Theorem

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...

An Application of φ-Metric and Related Best Proximity Point Results Generalizing Wardowski’s Fixed Point Theorem

Published Online: Jun 18, 2024

Page range: -

Received: Dec 08, 2023

Accepted: May 11, 2024

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

Keywords
-metric space, -best proximity point, ℱ-proximal contraction, Wardowski’s fixed point theorem

© 2024 Abhishikta Das et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

An Application of φ-Metric and Related Best Proximity Point Results Generalizing Wardowski’s Fixed Point Theorem

Published Online: Jun 18, 2024

Page range: -

Received: Dec 08, 2023

Accepted: May 11, 2024

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

Keywords-metric space, -best proximity point, ℱ-proximal contraction, Wardowski’s fixed point theorem

© 2024 Abhishikta Das et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
-metric space, -best proximity point, ℱ-proximal contraction, Wardowski’s fixed point theorem