Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation
The purpose of this article is to discuss some new aspects of the vector-valued metric space. The idea of an arbitrary binary relation along with the well-known <i>F</i> contraction is used to demonstrate the existence of fixed points in the context of a complete vector-valued metric spa...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/238 |
| _version_ | 1797431441435394048 |
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| author | Fahim Ud Din Muhammad Din Umar Ishtiaq Salvatore Sessa |
| author_facet | Fahim Ud Din Muhammad Din Umar Ishtiaq Salvatore Sessa |
| author_sort | Fahim Ud Din |
| collection | DOAJ |
| description | The purpose of this article is to discuss some new aspects of the vector-valued metric space. The idea of an arbitrary binary relation along with the well-known <i>F</i> contraction is used to demonstrate the existence of fixed points in the context of a complete vector-valued metric space for both single- and multi-valued mappings. Utilizing the idea of binary relation, and with the help of <i>F</i> contraction, this work extends and complements some of the very recently established Perov-type fixed-point results in the literature. Furthermore, this work includes examples to justify the validity of the given results. During the discussion, it was found that some of the renowned metrical results proven by several authors using different binary relations, such as partial order, pre-order, transitive relation, tolerance, strict order and symmetric closure, can be weakened by using an arbitrary binary relation. |
| first_indexed | 2024-03-09T09:45:03Z |
| format | Article |
| id | doaj.art-b90aff5119874e87877269dd9610bb42 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:45:03Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b90aff5119874e87877269dd9610bb422023-12-02T00:39:17ZengMDPI AGMathematics2227-73902023-01-0111123810.3390/math11010238Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary RelationFahim Ud Din0Muhammad Din1Umar Ishtiaq2Salvatore Sessa3Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanOffice of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54782, PakistanDipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, ItalyThe purpose of this article is to discuss some new aspects of the vector-valued metric space. The idea of an arbitrary binary relation along with the well-known <i>F</i> contraction is used to demonstrate the existence of fixed points in the context of a complete vector-valued metric space for both single- and multi-valued mappings. Utilizing the idea of binary relation, and with the help of <i>F</i> contraction, this work extends and complements some of the very recently established Perov-type fixed-point results in the literature. Furthermore, this work includes examples to justify the validity of the given results. During the discussion, it was found that some of the renowned metrical results proven by several authors using different binary relations, such as partial order, pre-order, transitive relation, tolerance, strict order and symmetric closure, can be weakened by using an arbitrary binary relation.https://www.mdpi.com/2227-7390/11/1/238Perov fixed pointordered theoretic Perov fixed pointℱ contraction |
| spellingShingle | Fahim Ud Din Muhammad Din Umar Ishtiaq Salvatore Sessa Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation Mathematics Perov fixed point ordered theoretic Perov fixed point ℱ contraction |
| title | Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation |
| title_full | Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation |
| title_fullStr | Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation |
| title_full_unstemmed | Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation |
| title_short | Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation |
| title_sort | perov fixed point results on f contraction mappings equipped with binary relation |
| topic | Perov fixed point ordered theoretic Perov fixed point ℱ contraction |
| url | https://www.mdpi.com/2227-7390/11/1/238 |
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