Convex functions, subdifferentiability and renormings |
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| Authors: | Cheng Lixin Wu Congxin Xue Xiaoping Yao Xiabo |
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| Affiliation: | (1) Nankai Institute of Mathematics, Nankai University, 300071 Tianjin, China;(2) Department of Mathematics, Harbin Institute of Technology, 150006 Harbin, China |
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| Abstract: | This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces. Supported by NSFC |
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| Keywords: | Convex function Differentiability Renorming Uniformly convex Banach space |
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