Global Approximation of Convex Functions by Differentiable Convex Functions on Banach Spaces.

Impacto

Downloads

Downloads per month over past year



Azagra Rueda, Daniel and Mudarra, C. (2015) Global Approximation of Convex Functions by Differentiable Convex Functions on Banach Spaces. Journal of Convex Analysis, 22 (4). pp. 1197-1205. ISSN 0944-6532

[thumbnail of Azagra34libre.pdf]
Preview
PDF
135kB
[thumbnail of Azagra34.pdf] PDF
Restringido a Repository staff only

117kB

Official URL: http://www.heldermann-verlag.de/jca/jca22/jca1499_b.pdf




Abstract

We show that if X is a Banach space whose dual X* has an equivalent locally uniformly rotund (LUR) norm, then for every open convex U subset of X, for every real number epsilon > 0, and for every continuous and convex function f : U -> R (not necessarily bounded on bounded sets) there exists a convex function g : U -> R of class C-1 (U) such that f - epsilon <= g <= f on U. We also show how the problem of global approximation of continuous (not necessarily bounded on bounded sets) convex functions by C-k smooth convex functions can be reduced to the problem of global approximation of Lipschitz convex functions by C-k smooth convex functions.


Item Type:Article
Uncontrolled Keywords:Approximation; Convex function; Differentiable function; Banach space
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:36175
Deposited On:01 Apr 2016 11:54
Last Modified:01 Apr 2016 11:54

Origin of downloads

Repository Staff Only: item control page