The skew generalized Von Neumann Jordan constant in the unit sphere
| Autor: | Wang, Yuxin, Liu, Qi, Xia, Jinyu, Huang, Shuaizhe |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | J.Hasty Results 1 (2008) 1-9; Erratum: J.Hasty Results 2 (2008) 1-2 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/S0550-3213(01)00405-9 |
| Popis: | 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 |
| Databáze: | arXiv |
| Externí odkaz: |
|