Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space
The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approxi...
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| Format: | Article |
| Language: | English |
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University of Baghdad, College of Science for Women
2023-10-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7509 |
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| author | Raghad I. Sabri Buthainah A. A. Ahmed |
| author_facet | Raghad I. Sabri Buthainah A. A. Ahmed |
| author_sort | Raghad I. Sabri |
| collection | DOAJ |
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The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced. After that, the best proximity point theorem for such type of mapping in a fuzzy normed space is state and prove. In addition, the idea of α ̃–ϕ ̃-proximal contractive mapping is presented in a fuzzy normed space and under specific conditions, the best proximity point theorem for such type of mappings is proved. Furthermore, some examples are offered to show the results' usefulness.
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| format | Article |
| id | doaj-art-e360e62551ac4edaa2c8a21be89bab72 |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-e360e62551ac4edaa2c8a21be89bab722025-08-20T03:39:28ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862023-10-0120510.21123/bsj.2023.7509Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed SpaceRaghad I. Sabri0Buthainah A. A. Ahmed 1Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq. The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced. After that, the best proximity point theorem for such type of mapping in a fuzzy normed space is state and prove. In addition, the idea of α ̃–ϕ ̃-proximal contractive mapping is presented in a fuzzy normed space and under specific conditions, the best proximity point theorem for such type of mappings is proved. Furthermore, some examples are offered to show the results' usefulness. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7509Best proximity point, Fuzzy normed space, α ̃- Proximal admissible mapping, α ̃–ψ ̃-Proximal contractive mapping, α ̃–ϕ ̃-Proximal contractive |
| spellingShingle | Raghad I. Sabri Buthainah A. A. Ahmed Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space مجلة بغداد للعلوم Best proximity point, Fuzzy normed space, α ̃- Proximal admissible mapping, α ̃–ψ ̃-Proximal contractive mapping, α ̃–ϕ ̃-Proximal contractive |
| title | Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space |
| title_full | Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space |
| title_fullStr | Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space |
| title_full_unstemmed | Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space |
| title_short | Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space |
| title_sort | best proximity point theorem for α ̃ ψ ̃ contractive type mapping in fuzzy normed space |
| topic | Best proximity point, Fuzzy normed space, α ̃- Proximal admissible mapping, α ̃–ψ ̃-Proximal contractive mapping, α ̃–ϕ ̃-Proximal contractive |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7509 |
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