Fixed points of set valued mappings in terms of start point on a metric space endowed with a directed graph (Q2359595)

Summary: 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.