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Article

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

by and *,†
Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Pasquale Vetro
Mathematics 2017, 5(2), 24; https://doi.org/10.3390/math5020024
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)
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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MDPI and ACS Style

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. https://doi.org/10.3390/math5020024

AMA Style

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(2):24. https://doi.org/10.3390/math5020024

Chicago/Turabian Style

Neog, Murchana; Debnath, Pradip. 2017. "Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph" Mathematics 5, no. 2: 24. https://doi.org/10.3390/math5020024

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