Global and fine approximation of convex functions
نویسندگان
چکیده
منابع مشابه
Global and Fine Approximation of Convex Functions
Let U ⊆ R be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f : U → R can be approximated by real analytic convex functions, uniformly on all of U . We also show that C-fine approximation of convex functions by smooth (or real analytic) convex functions on R is possible in general if and only if d = 1. Nevertheless, for d ≥ 2 we give a characterizat...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2013
ISSN: 0024-6115
DOI: 10.1112/plms/pds099