SOME FUNCTION CLASSES RELATED TO THE CLASS OF CONVEX FUNCTIONS
SOME FUNCTION CLASSES RELATED TO THE CLASS OF CONVEX FUNCTIONS
复制标题
DOI：
10.2140/pjm.1962.12.1203
复制
发表时间：
1962-12
影响因子：
0.6
通讯作者：
A. Bruckner;E. Ostrow
中科院分区：
文献类型：
--
作者：
A. Bruckner;E. Ostrow
Hille和Phillips[5]和R.A.Rosenbaum[7]等人已经研究过这些函数，更确切地说，它们的负数是次加的。在本文中，我们将主要讨论介于这两类函数之间的函数类，它们由弱于(1)但强于(2)的不等式定义。我们得到了严格的类层次结构和这些类的各种刻画性质，并研究了一个简单的平均运算，它将每个类变换成一个更小的类。
These functions, more precisely their negatives which are subadditive, have been studied by Hille and Phillips [5] and R. A. Rosenbaum [7] among others. In the paper we shall be concerned, in large part, with classes of functions that properly lie between these two classes and which are defined by inequalities which are weaker than (1) but stronger than (2). We obtain a strict hierarchy of classes and various characterizing properties of these classes and study a simple averaging operation that transforms each class into a smaller class.