A new extension to the controlled metric type spaces endowed with a graph

In this paper, we initiate a new extension of b-metric spaces, called controlled metric-like spaces, by changing the condition and that means basically we may have a non-zero self-distance. We prove some fixed point theorems which generalize many results in the literature. Also, we present an interesting application to illustrate our results by considering controlled metric-like spaces endowed with a graph.

Automated summary

In this paper, a new extension of b-metric spaces called controlled metric-like spaces is introduced by changing the condition to allow for a non-zero self-distance. Several fixed point theorems are proven, which generalize existing results, along with an application involving controlled metric-like spaces endowed with a graph.