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- Title
Best Proximity Point Theorem for α ̃–ψ ̃−Contractive Type Mapping in Fuzzy Normed Space.
- Authors
Sabri, Raghad I.; Ahmed, Buthainah A. A.
- Abstract
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.
- Subjects
NORMED rings; PROBLEM solving
- Publication
Baghdad Science Journal, 2023, Vol 20, Issue 5, p1722
- ISSN
2078-8665
- Publication type
Article
- DOI
10.21123/bsj.2023.7509