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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. 11971205. ISSN 09446532

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Official URL: http://www.heldermannverlag.de/jca/jca22/jca1499_b.pdf
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http://www.heldermannverlag.d  Publisher 
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 C1 (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 Ck smooth convex functions can be reduced to the problem of global approximation of Lipschitz convex functions by Ck 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 
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