Banach空间上凸函数的一致可微性

Uniform differentiability of convex functions on Banach space

1987年J.M.Borvein和D.Preiss对凸函数的Frechet可微性和Gsteaux可微性的定义给予了推广。本文在以上工作基础上定义了β—可微空间和弱β—可微空间,并主要讨论了弱β—可微空间。对β—可微空间的讨论参看(3).

In this paper we discuss the β—differentiability of convex functions on Banaeh space, it is a generalization of Frechet differentiability and Gateaux differentiability. We define weak β—differentiable spaces and obtain one necessary and sufficient condition for a weak β—differentiable space.