幂平均的凸组合界

  • 孟祥菊 ,
  • 田淑环 ,
  • 许会峰
展开
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

收稿日期: 2016-11-25

  网络出版日期: 2017-09-25

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

Received date: 2016-11-25

  Online published: 2017-09-25

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.

本文引用格式

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 . DOI: 10.3969/j.issn.1000-1565.2017.05.002

Abstract

The optimal value of parameters are obtained to make the following double inequality holds for all a,b>0,2Mr(a,b)≥G(a,b)+C(a,b)and A(a,b)+C(a,b)≥2Mr(a,b)where Mr(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.

参考文献

[1] SEIFFERT H J.Aufgabe 16[J].Die Wurzel,1995,29(87):221-222.
[2] STOLARSKY K B.The power and generalized logarithmic means[J].The American Mathematical Monthly,1980,87(7):545-548.
[3] CHU Y M,ZONG C,WANG G D.Optimal convex combination bounds of Seiffert and geometric means for the arithmetic mean[J].J Math Inequal,2011,5(3):429-434.
[4] RICHARDS K C.Sharp power mean bounds for the Gaussian hypergeometric function[J].Journal of Mathematical Analysis and Applications,2005,3089(1):303-313.
[5] CHU Y M,WANG M K,WANG G D.The optimal generalized logarithmic Mean boundcs for seiffert’s mean[J].Acta Mathematica Scientia,2012,32B(4):1619-1626.
[6] 孟祥菊,潘学功,高梦涵.对数平均的最优凸组合界[J].河北大学学报(自然科学版),2014,34(5):471-474.DOI:10.3969/j.issn.1000-1565.2014.05.005 MENG X J, PAN X G, GAO M H.Optimal convex combination bounds for logarithmic mean[J].Journal of Hebei University(Natural Science Edition),2014,34(5):471-474.DOI:10.3969/j.issn.1000-1565.2014.05.005
[7] 赵铁洪,褚玉明.对数平均和双参数广义Muirhead平均之间的比较[J].中国科学:数学,2015,45(3):233-244. ZHAO T H,CHU Y M.Comparison between the logarithmic and two-parameter generalized Muirhead means[J].Science China(mathematics),2015,45(3):233-244.
[8] 史明宇,褚玉明,蒋月评.关于幂平均、调和平均和指数平均的最佳不等式[J].数学物理学报,2011,31A(5):1377-1384. SHI M Y,CHU Y M,JIANG Y P.Optimal inequalities related to the power, harmonic and identric means[J].Acta Mathematica Scientia,2011,31A(5):1377-1384.
[9] 孙惠,褚玉明.Toader平均的二次与调和平均界[J].数学物理学报,2015,35A(1):36-42. SUN H, CHU Y M. Bounds for toader mean by quadratic and harmonic means[J].Acta Mathematica Scientia,2015,35A(1):36-42.
文章导航

/

〈 〉