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

Authors : Shaban Sedghi, Merryam Sımkha, Utku Gürdal, Ali Mutlu

Pages : 29-43

Doi:10.47086/pims.1442731

View : 14 | Download : 43

Publication Date : 2024-06-30

Article Type : Research

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