凸函数的β可微性和光滑模

The β-Differentiability of Convex Functions and Continuous Moduli

本文引入一类特殊的实值函数(模),并由此对Banach空间上凸函数的Fréchet可微性,更一般地,β-可微性进行了特征刻画.

In this thesis we introduce a type of special real functions called differentiahility moduli, and characterize the Fréchet differentiability and more generally, the β-differentiability of the convex functions on Banach spaces hy such moduli.