New geometric properties of Banach spaces |
| |
| Authors: | Kichi‐Suke Saito Ryotaro Tanaka |
| |
| Affiliation: | 1. Department of Mathematics, Faculty of Science, Niigata University, Niigata, Japan;2. Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, Japan |
| |
| Abstract: | In this paper, we introduce new geometric properties as generalizations of p‐uniform smoothness and q‐uniform convexity of Banach spaces. Furthermore, using generalized Beckner's inequality, we characterize the properties in terms of norm inequalities. As an application, we consider the duality relation. |
| |
| Keywords: | Absolute norms ψ ‐uniform smoothness ψ *‐uniform convexity Generalized Beckner's inequalities 46B20 |
|
|
