Convex Functions, Subdifferentiability and Renormings  

作　　者：Cheng Lixin Wu Congxin Xue Xiaoping Yao Xiaobo Nankai Institute of Mathematics, Nankai University, Tianjin 300071, China Department of Mathematics, Harbin Institute of Technology, Harbin 150006, China 

出　　处：《Acta Mathematica Sinica,English Series》1998年第1期47-56,共10页数学学报（英文版）

基　　金：NSFC

摘　　要：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.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.

关 键 词：Convex function Differentiabilit RENORMING Uniformly convex Banach space 

分 类 号：O1[理学—数学]