发表机构
Guangxi University（广西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对GV-模糊度量空间，构造了同时为GS-压缩与严格模糊ψ-压缩但非柯西的序列，否定了两个相关开放问题，表明模糊不动点定理需补充额外结构条件。
AI 中文摘要
经典的Banach原理依赖于压缩序列为柯西序列。Gregori与Sapena于2002年建立了模糊类比结果，但将此作为额外假设，留下了一个开放问题。Gregori等人于2020年随后提出，严格模糊ψ-压缩序列是否必然为柯西序列。我们通过一个反例否定地解决了这两个问题：在构造的GV-模糊度量空间中，存在一个序列既是GS-压缩的又是严格模糊ψ-压缩的，但并非柯西序列。这表明在一般GV-模糊度量空间中，压缩性绝不蕴含柯西性，模糊不动点定理中的额外结构条件是不可或缺的。
英文摘要
The classical Banach principle relies on contractive sequences being Cauchy. Gregori and Sapena (2002) established a fuzzy analogue but required this as an extra hypothesis, leaving it as an open problem. Gregori et al. (2020) later asked whether strictly fuzzy $ψ$-contractive sequences are necessarily Cauchy. We settle both problems negatively via a single counterexample: in a constructed GV-fuzzy metric space, there exists a sequence which is both GS-contractive and strictly fuzzy $ψ$-contractive, yet not Cauchy. This shows that contractivity never implies Cauchyness in general GV-fuzzy metric spaces, and additional structural conditions in fuzzy fixed point theorems are indispensable.
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