基于广义对数均值的算术 - 几何均值和托阿德均值的最优界
Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean.
作者信息
Ding Qing, Zhao Tiehong
机构信息
College of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha, 410205 China.
Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121 China.
出版信息
J Inequal Appl. 2017;2017(1):102. doi: 10.1186/s13660-017-1365-4. Epub 2017 May 5.
In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two positive numbers and , respectively.
在本文中，我们找到了最大值[公式：见正文]和最小值[公式：见正文]，使得双重不等式[公式：见正文]和[公式：见正文]对于所有满足[公式：见正文]的[公式：见正文]都成立，其中[公式：见正文]、[公式：见正文]和[公式：见正文]分别是两个正数[公式：见正文]和[公式：见正文]的算术 - 几何均值、托阿德均值和广义对数均值。
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