托阿德型均值的几何均值与纽曼均值的最优凸组合界
Optimal convex combination bounds of geometric and Neuman means for Toader-type mean.
作者信息
Yang Yue-Ying, Qian Wei-Mao
机构信息
School of Mechanical and Electrical Engineering, Huzhou Vocational & Technical College, Huzhou, 313000 China.
School of Distance Education, Huzhou Broadcast and TV University, Huzhou, 313000 China.
出版信息
J Inequal Appl. 2017;2017(1):201. doi: 10.1186/s13660-017-1473-1. Epub 2017 Aug 29.
In this paper, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] with [Formula: see text] if and only if [Formula: see text], [Formula: see text] , [Formula: see text] and [Formula: see text] , where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text] are the Toader, geometric, arithmetic and two Neuman means of and , respectively.
在本文中，我们证明了双重不等式[公式：见正文]对于所有满足[公式：见正文]的[公式：见正文]成立，当且仅当[公式：见正文]，[公式：见正文]，[公式：见正文]以及[公式：见正文]，其中[公式：见正文]，[公式：见正文]，[公式：见正文]以及[公式：见正文]，[公式：见正文]分别是[具体两个数]的托阿德均值、几何均值、算术均值以及两个诺伊曼均值。
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