Abstract
In this article, we present an extension of the controlled rectangular b-metric spaces, so-called controlled rectangular metric-like spaces, where we keep the symmetry condition and we only change the condition [D(s,r)=0⇔s=r]to[D(s,r)=0⇒s=r], which means we may have a non-zero self distance; also, D(s,s) is not necessarily less than D(s,r). This new type of metric space is a generalization of controlled rectangular b-metric spaces and partial rectangular metric spaces.