Derivative Type Mapping Theorem for the Interpolative Berinde Weak Contraction in Metric Spaces with Application

TL;DR

This paper establishes a fixed point theorem for derivative type mappings in metric spaces, extending existing concepts and applying the results to Fredholm integral equations.

Contribution

It introduces a fixed point theorem for interpolative Berinde weak contractions in metric spaces, expanding the scope of derivative type fixed point results.

Findings

Proved a new fixed point theorem for derivative type mappings.

Provided an example illustrating the main theorem.

Applied the theorem to solve a Fredholm integral equation.

Abstract

Olatinwo [3] introduced contractive definitions of the derivative type, and gave a new characterization of the Banach contraction principle, and fixed point theorems for contractions defined implicitly. On the other hand Ampadu et.al [4] introduced derivative type contractions in the setting of multiplicative metric spaces. In this paper, we have obtained a fixed point theorem of the derivative type for interpolative Berinde weak contractive mappings [2] in the setting of metric spaces. An examples is given to illustrate the main result of the paper. Finally, we apply our result to the Fredholm integral equation