AI 中文总结
该研究在Amini-Harandi等人的几何常数基础上，定义了斜参数化几何常数族，建立相关公式与条件，确定希尔伯特空间上的常数精确值，推导非方性等性质的条件，为检测巴拿赫空间相关几何性质提供统一框架。
AI 中文摘要
在Amini-Harandi和Rahimi引入的几何常数族基础上，我们通过用旋转系数对替代经典对称对，在实赋范空间上定义了一个斜参数化族。该修正揭示了新的极值行为，尤其针对非对称齐次权函数。我们建立了约化公式、比较不等式及参数稳定性估计。在适当的微分平衡条件下，确定了这些常数在希尔伯特空间上的精确值，并得到了维数至少为3时的逆刻画。进一步推导了一致非方性与正规结构的充分条件，以及经典赋范空间中的显式计算。这些结果为检测巴拿赫空间的希尔伯特型性质及与不动点相关的几何性质提供了统一框架。
英文摘要
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.
