摘要
凸函数是一类特殊的函数,随着其在应用上的不可替代性作用的逐渐显现,近年来,关于凸函数的研究已成为一个备受关注的热点,不同种类的凸函数概念被不断提出,尤其是基于区间上的二元幂平均确定的凸函数。考虑由区间上的算术平均、几何平均、调和平均所确定的调和凸函数、HG-凸函数、HA-凸函数等凸函数的推广问题,定义了HM-凸函数;通过对HM-凸函数的凸性特征的系统研究,讨论了HM-凸函数的判定方法并给出了相应的判定定理;分析了HM-凸函数的凸性特点,得到了若干凸性性质。在此基础上,建立了HM-凸函数的Jensen型不等式。
The convex function belongs to a special category of functions. Since its irreplaceable application within recentyears, the convex function study becomes attractive, while different categories of convex functions are brought forward,especially the brilliant convex function determined by dual parameters for two variables power means within a certainsection. Considering promotion issues of the harmonic convex function, HG-convex function and HA-convex functiondetermined by arithmetic means, geometric means and harmonic means within a certain section, this article gives thedetermination of HM-convex function, discusses its judgment method and the corresponding judgment theorem, andanalyzes its convexity features by systematically studying its convexity attribute. The author finally comes to severalconvexity properties of HM-convex function, and sets up the Jensen--type inequality of HM-convex function and theequivalent form.
出处
《沈阳师范大学学报（自然科学版）》
CAS
2015年第1期23-27,共5页
Journal of Shenyang Normal University:Natural Science Edition
基金
湖北省教育科学"十二五"规划项目(2013A054)
