Double controlled quasi metric-like spaces and some topological properties of this space

In present paper, we introduce a new extension of the double controlled metric-like spaces, so called double controlled quasi metric-like spaces "assuming that the self-distance may not be zero". Also, if the value of the metric is zero, then it has to be "a self-distance". After that, by using this new type of quasi metric spaces, we generalize many results in the literature and we prove fixed point theorems along with some examples illustrating.