Fuzzy n−Controlled Metric Space
This manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are give...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2023-09-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/2931 |
| _version_ | 1797404912369270784 |
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| author | Salman Furqan Naeem Saleem Salvatore Sessa |
| author_facet | Salman Furqan Naeem Saleem Salvatore Sessa |
| author_sort | Salman Furqan |
| collection | DOAJ |
| description | This manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are given to explain definitions and results. We define open ball, convergence of a sequence and a Cauchy sequence in the context of fuzzy n−controlled metric space. We also prove, by means of an example, that a fuzzy n−controlled metric space is not Hausdorff. At the end of the article, an application is given to prove the uniqueness of the solution to fractional differential equations. |
| first_indexed | 2024-03-09T03:01:57Z |
| format | Article |
| id | doaj.art-604695996f3a4ee6a87b5ad33e6a09b8 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-03-09T03:01:57Z |
| publishDate | 2023-09-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-604695996f3a4ee6a87b5ad33e6a09b82023-12-04T12:13:05ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392023-09-012110110110.28924/2291-8639-21-2023-1012316Fuzzy n−Controlled Metric SpaceSalman FurqanNaeem SaleemSalvatore SessaThis manuscript consists of the idea of n−controlled metric space in fuzzy set theory to generalize a number of fuzzy metric spaces in the literature, for example, pentagonal, hexagonal, triple, and double controlled metric spaces and many other spaces in fuzzy environment. Various examples are given to explain definitions and results. We define open ball, convergence of a sequence and a Cauchy sequence in the context of fuzzy n−controlled metric space. We also prove, by means of an example, that a fuzzy n−controlled metric space is not Hausdorff. At the end of the article, an application is given to prove the uniqueness of the solution to fractional differential equations.http://etamaths.com/index.php/ijaa/article/view/2931 |
| spellingShingle | Salman Furqan Naeem Saleem Salvatore Sessa Fuzzy n−Controlled Metric Space International Journal of Analysis and Applications |
| title | Fuzzy n−Controlled Metric Space |
| title_full | Fuzzy n−Controlled Metric Space |
| title_fullStr | Fuzzy n−Controlled Metric Space |
| title_full_unstemmed | Fuzzy n−Controlled Metric Space |
| title_short | Fuzzy n−Controlled Metric Space |
| title_sort | fuzzy n controlled metric space |
| url | http://etamaths.com/index.php/ijaa/article/view/2931 |
| work_keys_str_mv | AT salmanfurqan fuzzyncontrolledmetricspace AT naeemsaleem fuzzyncontrolledmetricspace AT salvatoresessa fuzzyncontrolledmetricspace |