强h-凸函数的若干性质

Some Properties of the Strongly h-Convex Function

强h-凸函数是强凸函数和h-凸函数的推广,而后者又是凸函数、s-凸函数、Godunova-Levin函数以及P-函数等的推广。本文讨论了强h-凸函数的一些基本性质,并结合上积函数,函数列收敛等概念,对强h-凸函数的性质进行更深入的讨论。

The strongly h-convex function is a generation of the convex function and the h-convex function, and the latter is also a common generalization of the convexity, s-convexity, the Godunova-Levin function and the P-function. In this paper, we discuss some basic properties of strongly h-convex functions, and make some presentations of them involving the notations of sup-multiplicative functions, convergence of sequence, etc.