Fixed Point Theorems for Contravariant Maps in Bipolar b-Metric Spaces with Integration Application

Year 2024, , 29 - 43, 30.06.2024

Shaban Sedghi Merryam Sımkha Utku Gürdal Ali Mutlu

https://doi.org/10.47086/pims.1442731

Abstract

As a natural extension of the metric and the bipolar metric, this article introduces the new abstract bipolar $b-$
metric. The bipolar $b-$metric is a novel technique addressed in this article; it is explained by combining the
well-known $b-$metric in the theory of metric spaces, as defined by Mutlu and G\"{u}rdal (2016) \cite{mg1}, with the
description of the bipolar metric. In this new definition, well-known mathematical terms such as Cauchy and
convergent sequences are utilized. In the bipolar $b-$metric, fundamental topological concepts are also defined to investigate the existence of fixed points implicated in such mappings under different contraction
conditions. An example is provided to demonstrate the presented results.

Keywords

bipolar b−metric space., complete b−metric space, Fixed point theory

Ethical Statement

All authors contributed equally and significantly in writing this article. All authors read and approved the manuscript. The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors.

Supporting Institution

This research received no external funding.

Thanks

No

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