Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space
In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduc...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/1712486 |
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| author | Mi Zhou Xiao-lan Liu Nicolae Adrian Secelean |
| author_facet | Mi Zhou Xiao-lan Liu Nicolae Adrian Secelean |
| author_sort | Mi Zhou |
| collection | DOAJ |
| description | In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature. |
| format | Article |
| id | doaj-art-24acd0ce633a4239985067abd5c91da4 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-24acd0ce633a4239985067abd5c91da42025-02-03T06:46:37ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/17124861712486Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric SpaceMi Zhou0Xiao-lan Liu1Nicolae Adrian Secelean2School of Science and Technology, University of Sanya, Sanya, Hainan 572000, ChinaCollege of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, ChinaDepartment of Mathematics and Informatics, Lucian Blaga University of Sibiu, Sibiu, RomaniaIn this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.http://dx.doi.org/10.1155/2020/1712486 |
| spellingShingle | Mi Zhou Xiao-lan Liu Nicolae Adrian Secelean Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space Journal of Mathematics |
| title | Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space |
| title_full | Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space |
| title_fullStr | Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space |
| title_full_unstemmed | Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space |
| title_short | Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space |
| title_sort | fixed point theorems for generalized kannan type mappings in a new type of fuzzy metric space |
| url | http://dx.doi.org/10.1155/2020/1712486 |
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