### 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

Preview |
PDF
135kB |

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