关键词: 凸函数;很光滑点:Gateaux可微, 逼近

Abstract:

In this paper, the authors prove that for every w^* lower semicontinuous Lipschitzian convex function on the dual of a bistrictly convexifiable Banach space can be uniformly approximated by a  sequence of w^* lower semicontinuous monotone nondecreasing Lipschitzian convex function with the dense very smooth point  set.

Key words: Convex function, Very smooth point, Gateaux differentiability, Approximation.