$\theta-\phi-$contraction on $\left(\alpha,\eta \right)-$complete rectangular $b-$ metric spaces

TL;DR

This paper introduces new fixed point theorems for generalized contractions in a novel class of rectangular b-metric spaces, extending and improving existing mathematical results with illustrative examples.

Contribution

The paper develops fixed point theorems for $ heta- ext{ extphi}$-contractions in $( ext{ extalpha}, ext{ exteta})$-complete rectangular $b$-metric spaces, broadening the scope of previous results.

Findings

Established new fixed point theorems for generalized contractions.

Extended existing results to a broader class of metric spaces.

Provided illustrative examples to demonstrate the theorems.

Abstract

In this paper, we present some fixed point results for generalized $\theta -\phi -$contraction in the framework of $\left( \alpha ,\eta \right)-$compete rectangular $b-$metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. The presented extend, generalize and improve existing results in the literature. Moreover, to support our main results we give an illustrative example.