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Mathematics 2017, 5(2), 24; doi:10.3390/math5020024

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

Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India
These authors contributed equally to this work.
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Academic Editor: Pasquale Vetro
Received: 28 June 2016 / Revised: 11 April 2017 / Accepted: 14 April 2017 / Published: 19 April 2017
(This article belongs to the Special Issue Fixed Point Theorems and Applications)
View Full-Text   |   Download PDF [263 KB, uploaded 19 April 2017]   |  

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. View Full-Text
Keywords: start point; fixed point; set valued mapping; metric space with a graph start point; fixed point; set valued mapping; metric space with a graph
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Neog, M.; Debnath, P. Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph. Mathematics 2017, 5, 24.

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