凸函数的次微分算子的一致连续性和一致单调性

Uniform Monotonicity and Uniform Continuity of Subdifferential Mappings of Convex Functions

该文给出了“有界—凸集—一致有界”（ｂ．ｃ．ｕ．ｂ），“有界—凸集—一致可微”（ｂ．ｃ．ｕ．ｄ）等概念．证明了凸函数及其次微分，微分在这些意义下的若干性质．建立了凸函数的次微分算子的单调性与该函数凸性关系的特征性质．

This note shows that a continuous convex function defined on an open convex set of a Banach space E is unifromly convex (uniformly Frechet differentiable,resp. )on the set if and only if its subdifferential map is uniformly monotone (uniformly continuous,resp. ).