%0 Journal Article
%A Azagra Rueda, Daniel
%A Mudarra, C.
%T Global Approximation of Convex Functions by Differentiable Convex Functions on Banach Spaces.
%D 2015
%@ 0944-6532
%U https://hdl.handle.net/20.500.14352/35103
%X 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.
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