Approximation of Convex Functions on the Dual of Banach Spaces

Abstract

AbstractThis paper shows that every w*-lower semicontinuous Lipschitzian convex function on the dual of a locally uniformly convexifiable Banach space, in particular, the dual of a separable Banach space, can be uniformly approximated by a generically Fréchet differentiable w*-lower semicontinuous monotone-nondecreasing Lipschitzian convex function sequenc