Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Antonio Francisco Roldán López de Hierro, Andreea Fulga, Erdal Karapınar and Naseer Shahzad
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Antonio Francisco Roldán López de Hierro: Department of Statistics and Operations Research, University of Granada, 18010 Granada, Spain
Andreea Fulga: Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, 500036 Brasov, Romania
Erdal Karapınar: Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot 820000, Binh Duong, Vietnam
Naseer Shahzad: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2021, vol. 9, issue 14, 1-13

Abstract: Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.

Keywords: fuzzy metric; fuzzy metric space; fixed point; Proinov-type theorem; non-Archimedean space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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