概率赋范空间中一类线性泛函的Hahn-Banach定理及应用

The Hahn-Banach Theorem for a Class of Linear Functional on Probabilistic Normed Spaces and the Application

本文用新的方式定义了概率赋范空间中一类有界线性算子的概率范数,证明了一类线性泛函的保概率范数延拓定理,应用这个定理证明了一类Gateaux 可微非线性算子的概率有限增量定理。

In this paper the new definition of probabilistic norm for a dass oflinear bounded operators on probabilistic normed spaces are defined.TheHahn-Banach Theorem for a dass of linear functional on probabilistic normedspaces are proved.This Hahn-Banach Theorem is also used in the theory of the differentionabout nonlinear operators.