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Fengshuo Xu

Publications and source records attributed to Fengshuo Xu.

4 recordsLinked to original sources
arXiv2026

On fuzzy contractions in fuzzy metric spaces

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 $\psi$-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 $\psi$-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.

math.GN↗
arXiv2026

A note on definable endomorphisms of ordered abelian groups

We answer Kourovka Notebook Problem~18.16 affirmatively in the pure language of ordered abelian groups, with parameters allowed. The piecewise-affine description of definable functions reduces the question to an algebraic rigidity theorem: an additive endomorphism of a torsion-free abelian group that is covered by finitely many rational-affine laws has one global rational slope. The parameter-free pure-language case is included, whereas the unrestricted expansion-language variant admits a simple counterexample.

math.LO↗
arXiv2023

Classification of maximally non-self-dual modular categories of small dimension

We prove that a non-pointed maximally non-self-dual (MNSD) modular category of Frobenius-Perron (FP) dimension less than $2025$ has at most two possible types, and all these types can be realized except those of FP dimension $675$, $729$ and $1125$. We also prove that all these modular categories are group-theoretical except the modular categories of dimension $675$. Our result shows that a non-group-theoretical MNSD modular category of smallest FP dimension may be the category of FP dimension $675$, and non-pointed MNSD modular category of smallest FP dimension is the category of FP dimension $243$.

math.QA↗