Certain Interpolative Proximal Contractions, Best Proximity Point Theorems in Bipolar Metric Spaces with Applications

Abstract

In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results.

Keywords

• bipolar metric space
• interpolative proximal-type contractions
• best proximity points
• fixed points
• existence and uniqueness