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Let H be a Hilbert space, E?H be an arbitrary subset and f:E?R, G:E?H be two functions. We give a necessary and sufficient condition on the pair (f,G) for the existence of a convex function F?C1,1(H) such that F=f and ?F=G on E. We also show tha[...]texto impreso
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 [...]texto impreso
Let C be a subset of ?n (not necessarily convex), f : C ? R be a function and G : C ? ?n be a uniformly continuous function, with modulus of continuity ?. We provide a necessary and sufficient condition on f, G for the existence of a convex func[...]
