On Fixed Point Theorems in Bipolar Metric Spaces Involving Polynomial-Type Contractions

TL;DR

This paper introduces new fixed point theorems in bipolar metric spaces using polynomial-type contractions, providing conditions for existence and uniqueness of fixed points, with generalizations over existing theorems.

Contribution

It presents novel fixed point results in bipolar metric spaces employing polynomial-type contractions, extending and improving prior fixed point theorems.

Findings

Established sufficient conditions for fixed point existence and uniqueness.

Provided illustrative examples demonstrating applicability.

Generalized and improved upon existing fixed point theorems.

Abstract

In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish sufficient conditions under which a mapping on a complete bipolar metric space admits a UFP. Several illustrative examples are provided to demonstrate the applicability of our theorems, and we further show how our results generalize and improve upon existing fixed point theorems in both standard and generalized metric settings.