关于Banach空间中连续凸函数的Gateaux可微性的一个注记

A Note to Gateaux Differentiability of the Convex Continuous Function on Banach Space

通过引进了范—ω＊一致连续的定义，指出了若Ｂａｎａｃｈ空间Ｘ中每个开凸子集Ｄ上定义的连续凸函数ｆ（ｘ）的次微分在Ｄ的一个稠集上范—ω＊一致连续，则ｆ（ｘ）一定在Ｄ的一个稠Ｇδ集上Ｇａｔｅａｕｘ可微。

The definition of norm ω * consistence continuity is introduced in this paper.It is shown that if the secondary derivative of a convex continuous function on banach space defined on an open convex subset of D is norm ω * consistence continuity on a dense subset of its domain,the function is gateaux differentiable on a dense G δ subset .