关于$h$ -凸函数的一个注记
A note on $h$-convex functions
摘要：
本文通过引入$h$-凸曲线（$h$ -cord）的概念，讨论了$h$ -凸函数的连续性.给出了$h$ -凸性的几何解释。证明了对于$h$ -连续函数$f$，是$h$ -凸的当且仅当是$h$ -中凸的.一般地，我们证明了如果$f$是$h$ -凸的，那么$f$是$h$ -连续的.讨论了$h$ -凸性的导数特征.
英文摘要：
In this work, we discuss the continuity of $h$-convex functions by introducing the concepts of $h$-convex curves ($h$-cord). Geometric interpretation of $h$-convexity is given. The fact that for a $h$-continuous function $f$, is being $h$-convex if and only if is $h$-midconvex is proved. Generally, we prove that if $f$ is $h$-convex then $f$ is $h$-continuous. A discussion regarding derivative characterization of $h$-convexity is also proposed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
