Controlled rectangular metric type spaces and some applications to polynomial equations

Abstract

In this paper, we introduce a generalization of rectangular $b-$metric spaces, by changing the rectangular inequality as follows \begin{equation*} ρ(x,y)\le θ(x,y,u,v)[ρ(x,u)+ρ(u,v)+ρ(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.