Asymptotic Smoothness, Convex Envelopes and Polynomial Norms

2015/12/16 by Jaramillo, Jesús A., Gonzalo, Raquel, Yáñez, Diego · 1 citation
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1512.05407

openalex publication_date 2015/12/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We introduce a suitable notion of asymptotic smoothness on infinite dimensional Banach spaces, and we prove that, under some structural restrictions on the space, the convex envelope of an asymptotically smooth function is asymptotically smooth. Furthermore, we study convexity and smoothness properties of polynomial norms, and we obtain that a polynomial norm of degree N has modulus of convexity of power type N.

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• On proximal mappings with Young functions in uniformly convex Banach\n spaces

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