New fixed point theorems for $(\phi, F)-$contraction on rectangular b-metric spaces

TL;DR

This paper introduces new fixed point theorems for $(, F)$-contractions within $b$-rectangular metric spaces, extending the Banach contraction principle and improving existing results in the field.

Contribution

It develops the concept of $(, F)$-contraction specifically for $b$-rectangular metric spaces, broadening the scope of fixed point theory.

Findings

Established existence and uniqueness of fixed points under the new contraction conditions.

Generalized previous fixed point results to a broader class of spaces.

Provided conditions that improve upon existing fixed point theorems.

Abstract

The Banach contraction principle is the most celebrated fixed point theorem, it has been generalized in various directions. In this paper, inspired by the concept of $(\phi, F)-$contraction in metric spaces, introduced by Wardowski. We present the notion of $(\phi, F)-$contraction in $b-$rectangular metric spaces to study the existence and uniqueness of fixed point for the mappings in this spaces. Our results improve many existing results.