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.
Highlights
Fixed-point theory is currently one of the most active fields in the area of nonlinear analysis and even in mathematics in general
Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces that are able to translate to this framework the best advantages of the auxiliary functions due to the the abovementioned researcher
We introduced a novel family of contractions in the setting of nonArchimedean fuzzy metric spaces
Summary
Fixed-point theory is currently one of the most active fields in the area of nonlinear analysis and even in mathematics in general. 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 auxiliary functions due to the the abovementioned researcher In this context, we prove some fixed-point results that improve some previous theorems by using a very general class of restrictions on the involved functions. We describe some necessary background to develop the main contents
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