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GLOBAL APPROXIMATION OF CONVEX FUNCTIONS BY DIFFERENTIABLE CONVEX FUNCTIONS ON BANACH SPACES
| Content Provider | Semantic Scholar |
|---|---|
| Author | Azagra, Daniel Mudarra, Carlos |
| Copyright Year | 2014 |
| 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 ⊆ X, for every ε > 0, and for every continuous and convex function f : U → R (not necessarily bounded on bounded sets) there exists a convex function g : X → R of class C(U) such that f − ε ≤ g ≤ f on U. We also show how the problem of global approximation of continuous (not necessarily bounded on bounded sets) and convex functions by C smooth convex functions can be reduced to the problem of global approximation of Lipschitz convex functions by C smooth convex functions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://eprints.ucm.es/36175/1/Azagra34libre.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
