Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph.

In the present article, we introduce the new concept of start point in a directed graph and provide the characterizations required for a directed graph to have a start point. We also define the notion of a self path set valued map and establish its relation with start point in the setting of a metric space endowed with a directed graph. Further, some fixed point theorems for set valued maps have been proven in this context. A version of the Knaster-Tarski theorem has also been established using our results. [ABSTRACT FROM AUTHOR]