1. The skew generalized Von Neumann Jordan constant in the unit sphere
- Author
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Wang, Yuxin, Liu, Qi, Xia, Jinyu, and Huang, Shuaizhe
- Subjects
Mathematics - Functional Analysis ,46B20, 46C15 ,F.2.2 ,I.2.7 - Abstract
In this paper, we introduce a new constant for Banach spaces, denoted as $\widetilde{C}_{\mathrm{NJ}}^p(\xi, v, X)$. We provide calculations for both the lower and upper bounds of this constant, as well as its exact values in certain Banach spaces. Furthermore, we give the inequality relationship between the $\widetilde{C}_{\mathrm{NJ}}^p(\xi, v, X)$ constant and the other two constants. Besides, we establish an equivalent relationship between the $\widetilde{C}_{\mathrm{NJ}}^p(\xi, v, X)$ constant and the $\widetilde{C}_{\mathrm{NJ}}^{(p)}(X)$ constant. Specifically, we shall exhibit the connections between the constant $\widetilde{C}_{\mathrm{NJ}}^p(\xi, v, X)$ and certain geometric characteristics of Ba nach spaces, including uniform convexity and uniform nonsquareness. Additionally, a sufficient condition for uniform normal structure about the $\widetilde{C}_{\mathrm{NJ}}^p(\xi, v, X)$ constant is also established., Comment: 19 pages
- Published
- 2024
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