Best Proximity Point Results in Fuzzy Normed Spaces
Fixed point (briefly FP ) theory is a potent tool for resolving several actual problems since many problems may be simplified to the FP problem. The idea of Banach contraction mapping is a foundational theorem in FP theory. This idea has wide applications in several fields; hence, it has been develo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Magister Program of Material Sciences, Graduate School of Universitas Sriwijaya
2023-04-01
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| Series: | Science and Technology Indonesia |
| Subjects: | |
| Online Access: | https://sciencetechindonesia.com/index.php/jsti/article/view/711/317 |
| Summary: | Fixed point (briefly FP ) theory is a potent tool for resolving several actual problems since many problems may be simplified to the FP problem. The idea of Banach contraction mapping is a foundational theorem in FP theory. This idea has wide applications in several fields; hence, it has been developed in numerous ways. Nevertheless, all of these results are reliant on the existence and uniqueness of a FP on some suitable space. Because the FP problem could not have a solution in the case of non self-mappings,the idea of the best proximity point (briefly Bpp) is offered to approach the best solution. This paper investigates the existence and uniqueness of the Bpp of non self-mappings in fuzzy normed space(brieflyFNspace) to arrive at the best solution. Following the introduction of the definition of the Bpp, the existence, and uniqueness of the Bpp are shown in a FNs pace for diverse fuzzy proximal contractions such as 𝔅 ̃𝜓- fuzzy proximal contractive mapping and 𝔅h𝔍h- fuzzy proximal contractive mapping. |
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| ISSN: | 2580-4405 2580-4391 |