Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls
Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls
复制标题
Banach空间中与单位球内切四边形相关的几何常数
DOI：
10.3390/sym13071294
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Yongjin Li
中科院分区：
文献类型：
--
作者：
Asif Ahmad;Qi Liu;Yongjin Li
我们引入了一个新的几何常数Jin（X）的基础上的推广，这是对称的，有关的长度内接四边形的单位球。我们首先研究这个新系数的一些基本性质。其次，证明了对于Banach空间，Jin（X）成为16当且仅当范数是由内积导出的。此外，还研究了它的性质以及与其它已知几何常数之间的关系。最后给出了一个包含正规结构的充分条件。
We introduce a new geometric constant Jin(X) based on a generalization of the parallelogram law, which is symmetric and related to the length of the inscribed quadrilateral side of the unit ball. We first investigate some basic properties of this new coefficient. Next, it is shown that, for a Banach space, Jin(X) becomes 16 if and only if the norm is induced by an inner product. Moreover, its properties and some relations between other well-known geometric constants are studied. Finally, a sufficient condition which implies normal structure is presented.
影响因子：
0.8
作者：
Mikio Kato;L. Maligranda;Y. Takahashi
通讯作者：
Mikio Kato;L. Maligranda;Y. Takahashi