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arXiv · 2608.00933

Skew-Parameterized Geometric Constants in Banach Spaces

Qing Du·Wenwen Zhang·Zhiyao Fang·Qi Liu
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Abstract

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.

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Qing Du, Wenwen Zhang, Zhiyao Fang, Qi Liu. 2026-08-02. Skew-Parameterized Geometric Constants in Banach Spaces. https://arxiv.org/abs/2608.00933

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