Controlled rectangular metric type spaces and some applications to polynomial equations

TL;DR

This paper introduces a generalized rectangular b-metric space with a modified inequality, proves fixed-point theorems within this framework, and demonstrates applications to polynomial equations, opening new research directions.

Contribution

It presents a novel generalization of rectangular b-metric spaces with a variable coefficient and establishes fixed-point theorems for this new setting.

Findings

Established fixed-point theorems in the generalized space

Applied the results to solve polynomial equations

Proposed open questions for future research

Abstract

In this paper, we introduce a generalization of rectangular $b-$metric spaces, by changing the rectangular inequality as follows \begin{equation*} \rho(x,y)\le \theta(x,y,u,v)[\rho(x,u)+\rho(u,v)+\rho(v,y)], \end{equation*}% for all distinct$\ x,y,u,v\in X.$ We prove some fixed-point theorems and we use our results to present a nice application in last section of this paper. Moreover, in the conclusion we present some new open questions.