optimal common fixed point results in complete metric spaces with w-distance

In this article, we will study the existence and uniqueness of optimal common fixed points for self-mappings in metric spaces with w-distance. we obtain generalizations of the kocev and rakočević fixed point theorems. the obtained results do not require the continuity or the condition (c; k) of maps, but require the weaker condition (w). we also improve some of our results when the metric space is equipped with a w0-distance. in this way, we get new existence results for non-cyclic quasi-contraction mappings of the fisher type.