Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph
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 metri...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2227-7390/5/2/24 |
| _version_ | 1811233907209666560 |
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| author | Murchana Neog Pradip Debnath |
| author_facet | Murchana Neog Pradip Debnath |
| author_sort | Murchana Neog |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T11:27:55Z |
| format | Article |
| id | doaj.art-dd72c6a46f0f4d0d904b6e30a33f428d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-12T11:27:55Z |
| publishDate | 2017-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-dd72c6a46f0f4d0d904b6e30a33f428d2022-12-22T03:35:11ZengMDPI AGMathematics2227-73902017-04-01522410.3390/math5020024math5020024Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed GraphMurchana Neog0Pradip Debnath1Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, IndiaDepartment of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, IndiaIn 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.http://www.mdpi.com/2227-7390/5/2/24start pointfixed pointset valued mappingmetric space with a graph |
| spellingShingle | Murchana Neog Pradip Debnath Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph Mathematics start point fixed point set valued mapping metric space with a graph |
| title | Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph |
| title_full | Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph |
| title_fullStr | Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph |
| title_full_unstemmed | Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph |
| title_short | Fixed Points of Set Valued Mappings in Terms of Start Point on a Metric Space Endowed with a Directed Graph |
| title_sort | fixed points of set valued mappings in terms of start point on a metric space endowed with a directed graph |
| topic | start point fixed point set valued mapping metric space with a graph |
| url | http://www.mdpi.com/2227-7390/5/2/24 |
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