RT Journal Article
T1 Global Approximation of Convex Functions by Differentiable Convex Functions on Banach Spaces.
A1 Azagra Rueda, Daniel
A1 Mudarra, C.
AB 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.
PB Heldermann Verlag
SN 0944-6532
YR 2015
FD 2015
LK https://hdl.handle.net/20.500.14352/35103
UL https://hdl.handle.net/20.500.14352/35103
LA eng
NO Programa Internacional de Doctorado de la Fundacion La Caixa-Severo Ochoa
DS Docta Complutense
RD 9 abr 2025