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

Azagra Rueda, DanielMudarra, C.2023-06-192023-06-1920150944-6532https://hdl.handle.net/20.500.14352/35103We 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.engGlobal Approximation of Convex Functions by Differentiable Convex Functions on Banach Spaces.journal articlehttp://www.heldermann-verlag.de/jca/jca22/jca1499_b.pdfhttp://www.heldermann-verlag.drestricted access517.98ApproximationConvex functionDifferentiable functionBanach spaceAnálisis funcional y teoría de operadores