Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results
In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b-metric space, fuzzy b-metric space, and extended fuzzy b-metric space. We use f,g,h, three noncomparable functions as follows: mqμ,η...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9936992 |
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| _version_ | 1832567851487068160 |
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| author | Salman Furqan Hüseyin Işık Naeem Saleem |
| author_facet | Salman Furqan Hüseyin Işık Naeem Saleem |
| author_sort | Salman Furqan |
| collection | DOAJ |
| description | In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b-metric space, fuzzy b-metric space, and extended fuzzy b-metric space. We use f,g,h, three noncomparable functions as follows: mqμ,η,t+s+w≥mqμ,ν,t/fμ,ν∗mqν,ξ,s/gν,ξ∗mqξ,η,w/hξ,η. We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation. |
| format | Article |
| id | doaj-art-2ec5e47bab824fad86ab09e4567fd1f7 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-2ec5e47bab824fad86ab09e4567fd1f72025-02-03T01:00:16ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/99369929936992Fuzzy Triple Controlled Metric Spaces and Related Fixed Point ResultsSalman Furqan0Hüseyin Işık1Naeem Saleem2Department of Mathematics, University of Management and Technology, Lahore, PakistanFaculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, VietnamDepartment of Mathematics, University of Management and Technology, Lahore, PakistanIn this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b-metric space, fuzzy b-metric space, and extended fuzzy b-metric space. We use f,g,h, three noncomparable functions as follows: mqμ,η,t+s+w≥mqμ,ν,t/fμ,ν∗mqν,ξ,s/gν,ξ∗mqξ,η,w/hξ,η. We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation.http://dx.doi.org/10.1155/2021/9936992 |
| spellingShingle | Salman Furqan Hüseyin Işık Naeem Saleem Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results Journal of Function Spaces |
| title | Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results |
| title_full | Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results |
| title_fullStr | Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results |
| title_full_unstemmed | Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results |
| title_short | Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results |
| title_sort | fuzzy triple controlled metric spaces and related fixed point results |
| url | http://dx.doi.org/10.1155/2021/9936992 |
| work_keys_str_mv | AT salmanfurqan fuzzytriplecontrolledmetricspacesandrelatedfixedpointresults AT huseyinisık fuzzytriplecontrolledmetricspacesandrelatedfixedpointresults AT naeemsaleem fuzzytriplecontrolledmetricspacesandrelatedfixedpointresults |