非阿基米德模糊度量空间中（比之更一般）的模糊充分谱压缩
Fuzzy ample spectrum contractions in (more general than) non-Archimedean fuzzy metric spaces
摘要：
考虑到Roldán et al.的充分谱压缩在度量空间中推广和统一了十多个不同的压缩映射族，本文首次研究了在Kramosil和Michálek意义下的模糊度量空间的更一般框架中如何实现这一概念.我们引入两种不同的方法的概念，模糊充分谱压缩，我们证明了一般结果的存在性和唯一性的不动点。相对于以前的方法，所提出的概念具有以下优点：（1）它们允许在非常一般的模糊框架中发展不动点理论（例如，底层模糊空间不一定是完整的）;（2）我们所采用的方法能够克服Kramosil和Michálek在模糊度量空间中提出的技术缺陷（不出现在George和Veeramani意义下的模糊度量空间中）;（3）为了考虑比非阿基米德模糊度量空间更一般的情形，我们引入了模糊空间中非Cauchy序列的一个新性质;（4）与模糊充分谱压缩相关的压缩性条件不必用单独的变量表示;（5）这类模糊压缩算子推广了一些著名的模糊压缩算子族，使得所有的Mihet模糊$ψ$ -压缩算子类.由于这些性质，本研究给出了一个肯定的部分答案，作者几年前提出的一个问题。
英文摘要：
Taking into account that Roldán et al.'s ample spectrum contractions have managed to extend and unify more than ten distinct families of contractive mappings in the setting of metric spaces, in this manuscript we present a first study on how such concept can be implemented in the more general framework of fuzzy metric spaces in the sense of Kramosil and Michálek. We introduce two distinct approaches to the concept of fuzzy ample spectrum contractions and we prove general results about existence and uniqueness of fixed points. The proposed notions enjoys the following advantages with respect to previous approaches: (1) they permit to develop fixed point theory in a very general fuzzy framework (for instance, the underlying fuzzy space is not necessarily complete); (2) the procedures that we employ are able to overcome the technical drawbacks raising in fuzzy metric spaces in the sense of Kramosil and Michálek (that do not appear in fuzzy metric spaces in the sense of George and Veeramani); (3) we introduce a novel property about sequences that are not Cauchy in a fuzzy space in order to consider a more general context than non-Archimedean fuzzy metric spaces; (4) the contractivity condition associated to fuzzy ample spectrum contractions does not have to be expressed in separate variables; (5) such fuzzy contractions generalize some well-known families of fuzzy contractive operators such that the class of all Mihet's fuzzy $ψ$-contractions. As a consequence of these properties, this study gives a positive partial answer to a question posed by this author some years ago.
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