Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (3): 568-572.

• Articles • Previous Articles     Next Articles

Sharp Bounds for the first Seiffert and Logarithmic Means in Terms of Generalized Heronian Mean

 GAO Hong-Ya, GUO Jian-Ling, LI Meng-Hua   

  1. College of Mathematics and Computer Science, Hebei University, Hebei Baoding 071002
  • Received:2011-12-13 Revised:2013-01-09 Online:2013-06-25 Published:2013-06-25
  • Supported by:

    国家自然科学基金(10971224)和河北省自然科学基金(A2011201011)资助

Abstract:

We find the least values αγ and the greatest values βτ, such that the inequalities
Hα(a, b)<P(a, b)<Hβ (a, b) ; 和Hγ(a, b)<L(a, b)<Hτ(a, b)
hold for all a, b>0 with ab. Here, Hω(a, b), P(a, b), and L(a, b) be the generalized Heronian, the first Seiffert and the
logarithmic means of two positive numbers a and b, respectively.

Key words: Sharp bound, The first Seiffert mean, Logarithmic mean, Generalized Heronian mean

CLC Number: 

  • 26D15
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