In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...

In this paper, we introduce the notion of fuzzy R−ψ−contractive mappings and prove some relevant results on existence uniqueness fixed points for type in setting non-Archimedean metric spaces. Several illustrative examples are also given to support our newly proven results. Furthermore, apply main a solution Caputo fractional differential equations.

This paper addresses a problem of global optimization in non-Archimedean fuzzy metric space context without P-property. Specifically, it concerns the determination distance between two subsets space. Our approach to solving this is find an optimal approximate solution fixed point equation. has been well studied within category problems called proximity problems. We explore some new types (ψ−ϕ)-...

In this paper, we first consider the disjoint union of two fuzzy metric spaces and non-existence of fuzzy contractive maps. We prove that there exists a natural fuzzy metric on the disjoint union of two fuzzy metric spaces. We also show that there is a fuzzy metric space which does not admit any fuzzy contractive map. Second, we introduce the notion of a fuzzy diameter for fuzzy metric spaces a...

As other authors have been very interested in the topic of fixed points, we obtained some results this study that emphasize importance point theory. Kannan described a more general contraction than Banach took its name and later Reich generalized further metric spaces. In paper, introduced new contractions called type γ-contraction which are generalization for non-Archimedean fuzzy We presented...

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

in the present paper, a partial order on a non- archimedean fuzzymetric space under the  lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.