Various k-Smoothnesses of Norms on Banach Spaces |
Received:June 27, 1992 Revised:April 04, 1993 |
Key Words:
k-smoothness very k-smoothness Hahn-Banach smoothness.
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Abstract: |
We define a concept of very k-smoothness(kVS) for every natural number k, andgives the necessary and sufficient conditions for very k-smoothness to be k-smoothnessand weak Hahn-Banach smoothness (w (H-B)S).The results extend a conclusion of [3].Moreover, we give several equivalent conditions for k-smoothness, strong k-smoothness,uniform k-convexity, weak uniform k-convexity and weak uniform k-convexity. |
Citation: |
DOI:10.3770/j.issn:1000-341X.1995.02.016 |
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