Application of a New Class of Characteristic Function

Abstract

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.

Keywords

• banach spaces
• generalized modulus of convexity
• generalized modulus of smoothness
• uniformly convex
• uniformly smooth