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arXiv · 2505.17600

On some generalized geometric constants with two parameters in Banach spaces

Yuxin Wang·Qi Liu·Haoyu Zhou·Jinyu Xia·Muhammad Toseef
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Abstract

In this paper, we build upon the TX constant that was introduced by Alonso and Llorens-Fuster in 2008. Through the incorporation of suitable parameters, we have successfully generalized the aforementioned constant into two novel forms of geometric constants, which are denoted as T1({\lambda},\mu,X ) and T2(\k{appa},{\tau},X ). First, we obtained some basic properties of these two constants, such as the upper and lower bounds. Next, these two constants served as the basis for our characterization of Hilbert spaces. More significantly, our findings reveal that these two constants exhibit a profound and intricate interrelation with other well-known constants in Banach spaces. Finally, we characterized uniformly non-square spaces by means of these two constants.

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Yuxin Wang, Qi Liu, Haoyu Zhou, Jinyu Xia, Muhammad Toseef. 2025-05-23. On some generalized geometric constants with two parameters in Banach spaces. https://arxiv.org/abs/2505.17600

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