幂平均的凸组合界

doi:10.3969/j.issn.1000-1565.2017.05.002

河北大学学报(自然科学版) ›› 2017, Vol. 37 ›› Issue (5): 454-456.DOI: 10.3969/j.issn.1000-1565.2017.05.002

幂平均的凸组合界

孟祥菊,田淑环,许会峰

收稿日期:2016-11-25 出版日期:2017-09-25 发布日期:2017-09-25
作者简介:孟祥菊(1971—),女,河北卢龙人,保定学院副教授,主要从事几何函数论的研究. E-mail:mengxiangju328@163.com
基金资助:
河北省软科学基金资助项目(154576249);河北省自然科学基金资助项目(A2015201149)

Optimal convex combination bounds for the power mean

MENG Xiangju,TIAN Shuhuan,XU Huifeng

Department of Mathematics and Computer Science, Baoding College, Baoding 071000, China

Received:2016-11-25 Online:2017-09-25 Published:2017-09-25

摘要/Abstract

摘要： 得到了关于几何平均G(a,b)、反调和平均C(a,b)、幂平均Mr(a,b)和算术平均A(a,b)的不等式,对所有的a、b>0成立的γ的最佳值.

关键词: 幂平均, 几何平均, 反调和平均, 算术平均

Abstract: The optimal value of parameters are obtained to make the following double inequality holds for all a,b>0,2M_r(a,b)≥G(a,b)+C(a,b)and A(a,b)+C(a,b)≥2M_r(a,b)where M_r(a,b),G(a,b),C(a,b),A(a,b)denote the power mean,the geometric mean,the contraharmonic mean, the arithmetic mean of two different positive numbers a and b respectively.

Key words: the power mean, the geometric mean, the contraharmonic mean, the arithmetic mean

中图分类号:

O178

孟祥菊,田淑环,许会峰. 幂平均的凸组合界[J]. 河北大学学报(自然科学版), 2017, 37(5): 454-456.

MENG Xiangju,TIAN Shuhuan,XU Huifeng. Optimal convex combination bounds for the power mean[J]. Journal of Hebei University (Natural Science Edition), 2017, 37(5): 454-456.

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幂平均的凸组合界

Optimal convex combination bounds for the power mean

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[2]	潘学功,孟祥菊. 第1类反调和平均和对数平均的最优凸组合界[J]. 河北大学学报(自然科学版), 2013, 33(2): 124-126,147.
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