On uniformly convex functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:505

Article

Grelier, G.¹  Raja, M.¹ 

[1] Univ Murcia, Dept Matemat, Campus Espinardo, Murcia 30100, Spain

关键词: Uniform convexity;    Super weak compactness;   

DOI  :  10.1016/j.jmaa.2021.125442

来源: Elsevier

【 摘 要 】

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to obtain other remarkable properties such as the coercivity. Our techniques allow to retrieve Enflo's uniformly convex renorming of super-reflexive Banach spaces as the regularization of a raw function built from trees. Among other applications, we provide a sharp estimation of the distance of a given function to the set of differences of Lipschitz convex functions. Finally, we prove the equivalence of several possible ways to quantify the super weakly noncompactness of a convex subset of a Banach space. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free