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

Murchana Neog and Pradip Debnath
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Murchana Neog: Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India
Pradip Debnath: Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India

Mathematics, 2017, vol. 5, issue 2, 1-7

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.

Keywords: start point; fixed point; set valued mapping; metric space with a graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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