一类新特征函数的应用

Application of a New Class of Characteristic Function

在Banach空间中,考虑引入一类新的定义于[0,+∞)上,关于实数t的实特征函数fx+ty(y)和fx+ty(x),这类新特征函数的相应性质可以用于刻划Banach空间的许多几何性质。本文从这类新特征函数的角度出发,讨论了在Banach空间中,这类新特征函数与广义凸性模,广义光滑模之间新的等价形式,从而给出判断Banach空间一致凸,一致光滑的一种新方法。

In Banach space,considering introducing a new class of real characteristic functions fx+ty(y)and fx+ty(y),the independent variable is t,and the domain is[0,+∞),and the corresponding properties of those new characteristic functions are used to characterize many geometric properties of Banach spaces.This paper proceeds with the point of view of this new characteristic function.In this paper,we discuss a new equivalent of between such new characteristic functions and generalized modulus of convexity and generalized modulus of smoothness in Banach spaces.A new method of judging uniformly convex and uniformly smooth Banach spaces is given.