Global optimal solutions for proximal fuzzy contractions

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution x that is optimal in the sense that the error d(x,Tx) assumes the global minimum value d(A,B). In the present paper, we initiate some new classes of proximal contraction mappings...

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Bibliographic Details
Published inPhysica A Vol. 551; p. 123925
Main Authors Hussain, Nawab, Kutbi, M.A., Salimi, Peyman
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2020
Subjects
[formula omitted]-proximal contraction
Best approximate solution
Non-Archimedean fuzzy metric space
47H10
Non-Archimedean fuzzy metric space
65Q10
Best approximate solution
α-proximal contraction
65Q30
54H25
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Summary:Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution x that is optimal in the sense that the error d(x,Tx) assumes the global minimum value d(A,B). In the present paper, we initiate some new classes of proximal contraction mappings and obtain best proximity point theorems for such fuzzy mappings in a non-Archimedean fuzzy metric space. As outcomes of these theorems, we conclude evident new best proximity and fixed point theorems in non-Archimedean fuzzy metric spaces with partial order. Furthermore, we provide an example to elaborate the usability of the established results.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2019.123925