arXiv subjects

Zhiyao Fang

Publications and source records attributed to Zhiyao Fang.

6 recordsLinked to original sources

arXiv2026

A Fermat--Torricelli convex-hull characterization of inner-product spaces via Birkhoff--James orthogonality

The classical location problem posed by Weber [Über den Standort der Industrien,Tübingen: J. C. B. Mohr, 1909] has motivated various geometric characterizations of inner-product spaces. Benítez, Fernández and Soriano [Trans. Amer. Math. Soc. \textbf{354} (2002), 5027--5038] characterized real inner-product spaces through the convex-hull property of Fermat--Torricelli medians.Pakhrou [J. Funct. Anal. \textbf{285} (2023), 110078] further established a characterization using $γ$-centers and equilateral triangles. Building on these results, we show that the Fermat--Torricelli convex-hull criterion remains valid when restricted to triples satisfying a one-sided Birkhoff--James orthogonality condition.The proof combines norming functionals, radial rescaling,Alexandrov differentiability, and the area formula.No completeness, smoothness, or strict convexity assumptions are required.

math.FA↗

arXiv2026

An Improved Inequality between the von Neumann-Jordan and James Constants

We provide a strengthened answer to the questions posed by Alonso, Martín, and Papini [Studia Math. 188 (2008), 135--150] concerning the comparison between the von Neumann--Jordan and James constants . The classical inequality $\CNJ(X)\leq J(X)$ between the von Neumann--Jordan and James constants was established by Takahashi and Kato [J. Math. Anal. Appl. 359 (2009), 602--609], Wang [Proc. Amer. Math. Soc. 138 (2010), 695--701], and Yang and Li [Appl. Math. Lett. 23 (2010), 277--281], while related sharp estimates were obtained by Kato and Takahashi [Rend. Circ. Mat. Palermo (2) Suppl. 82 (2010), 75--91]. We sharpen this inequality to $\CNJ(X)\leq\JB(X)$, where $\JB(X)$ is the Birkhoff--James orthogonal James constant introduced by Baronti and Papini [Constr. Math. Anal. 5 (2022), 37--45]. Our proof employs optimal distance ellipses and alternating contact directions.

math.FA↗

arXiv2026

James-type constants for Birkhoff--James orthogonality and approximate isosceles

We introduce two James-type constants associated with approximate isosceles and approximate Birkhoff--James orthogonality in real normed spaces. The isosceles family coincides with the classical James constant of Gao and Lau [J. Austral. Math. Soc. Ser. A 48 (1990), 101--112], while the Birkhoff family extends the orthogonal James constant of Baronti and Papini [Constr. Math. Anal. 5 (2022), no.~1, 37--45]. We show that approximate orthogonality constraints can, in certain settings, recover classical geometric constants exactly. In particular, the approximate isosceles family collapses to the classical James constant, while the approximate Birkhoff--James family forms a genuine parameter-dependent interpolation between the orthogonal and classical James constants.We also compare the Birkhoff profile with several classical geometric constants and study how it changes with the parameter.Several examples are also given to illustrate the relation between geometric constants and approximate orthogonality.

math.FA↗

arXiv2026

Skew-Parameterized Geometric Constants in Banach Spaces

Building on the family of geometric constants introduced by Amini-Harandi and Rahimi, we define a skew-parameterized family on real normed spaces by replacing the classical symmetric pair with a rotated coefficient pair. This modification reveals new extremal behavior, particularly for asymmetric homogeneous weight functions. We establish reduction formulas, comparison inequalities, and parameter-stability estimates. Under an appropriate differential balance condition, we determine the exact values of these constants on Hilbert spaces and obtain a converse characterization in dimensions at least three. We further derive sufficient conditions for uniform non-squareness and normal structure, together with explicit computations in classical normed spaces. These results provide a unified framework for detecting Hilbertian and fixed-point-related geometric properties of Banach spaces.

math.FA↗

arXiv2026

A generalization of the $(α,β,γ)$ von Neumann-Jordan type constant in Banach spaces

In this paper,motivated by the pioneering work of Moslehian and Rassias, we introduce a novel generalized von Neumann-Jordan type constant in Banach spaces, a constant that notably encompasses a range of classical geometric constants. First, we establish the bounds of this constant within Banach spaces. Next, we derive its relationships with other geometric constants. Furthermore, we characterize the uniformly non-square property and provide a sufficient condition for the uniform normal structure by leveraging this newly proposed constant.

math.FA↗

arXiv2026

Some inequalities and geometric constants in p-normed spaces

In this paper, we study some geometric constants in complete $p$-normed spaces with $0 < p \leq 1$. We introduce a new symmetric geometric constant associated with isosceles orthogonality, establish its sharp bounds, and provide an orthogonal characterization of the generalized von Neumann-Jordan constant in such spaces. We also investigate two Milman-type moduli in complete $p$-normed spaces, including their fundamental properties and sharp product inequalities. Finally, we extend the relation between the James constant and the generalized von Neumann-Jordan constant .

math.FA↗