巴拿赫空间中(α,β,γ)型冯·诺依曼 - 乔丹常数的推广
A generalization of the $(α,β,γ)$ von Neumann-Jordan type constant in Banach spaces
浏览论文内容
中文总结 AI 辅助
受前人启发在巴拿赫空间引入新型广义冯·诺依曼 - 乔丹常数，确定其在巴拿赫空间中的界，推导与其他几何常数的关系，借此刻画一致非方性质并给出一致正规结构充分条件。
中文摘要 AI 辅助
本文受莫斯莱希安和拉西亚斯开创性工作的启发，在巴拿赫空间中引入了一种新型广义冯·诺依曼 - 乔丹常数，该常数包含一系列经典几何常数。首先确定了此常数在巴拿赫空间中的界，接着推导其与其他几何常数的关系，还利用该常数刻画了一致非方性质并给出一致正规结构的充分条件。
英文摘要
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.
