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

Abstract

Abstract: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.

Hypergraphical Metric Spaces and Fixed Point Theorems

“…Abbas et al [13] presented some fixed point results for set contractions on metric spaces with a directed graph. In 2017, Debanath and Neog [14] initiated the concept of start point on a metric space endowed with a directed graph. ey offered the alternate concept of start point in a directed graph and provided the characterizations which are necessary for a directed graph having start point.…”

New extension of some fixed point results in complete metric spaces

“…There have been many exciting developments in the field of existence and uniqueness of fixed points in various directions [1,5,6,8,9,10,13,16,17]. Srivastava et al [18,19] gave some interesting applications of fixed point theorems in fractional integral equations.…”