Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1377-1384.

• Articles • Previous Articles     Next Articles

Optimal Inequalities Related to the Power, Harmonic and Identric Means

 SHI Ming-Yu1, CHU Yu-Ming2, JIANG Yue-Ping3   

  1. 1.College of Mathematics and Computer Science, Hebei University, Hebei Baoding 071002;
    2.Department of Mathematics, Huzhou Teachers College, Zhejiang Huzhou 313000;
    3.College of Mathematics and Econometrics, |Hunan University, Changsha 410082
  • Received:2009-11-15 Revised:2010-12-06 Online:2011-10-25 Published:2011-10-25
  • Supported by:

    国家自然科学基金(11071069)、浙江省自然科学基金(Y7080106)和浙江高等学校创新团队基金

Abstract:

For any a, b>0 , the authors present the following two optimal inequalities: Hα(a, b)I1-α(a, b)≥M2-5α/3(a, b) for α∈(2/5,1), and Hα(a, b)I1-α(a, b)≤M2-5α/3(a, b) for α∈(1/25, 4/25). Here, H(a, b), I(a, b) and Mp(a, b) denote the harmonic, identric and power means of order of p of two positive numbers a and b, respectively.

Key words: Power mean, Identric mean, Harmonic mean

CLC Number: 

  • 26E60
Trendmd