  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.
