Asymptotic weighted approximation of convex functions

Advances in Applied Mathematics 2026 Open access

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Authors: Fernanda Moreira Baêta
DOI: 10.1016/j.aam.2026.103057
Cited by: 1
References: 8

Abstract

Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to infinity. These asymptotic expressions are formulated in terms of a functional that extends the notion of affine surface area to the functional setting.

Fields of Study & Subjects

Approximation Theory and Sequence Spaces Mathematical Inequalities and Applications Functional Equations Stability Results

Publication details

Journal / source
Advances in Applied Mathematics
Publisher
Elsevier BV
Volume
176
Pages
103057–103057
Publication date
9 February 2026
Language
EN