Acta mathematica scientia, Series B >
THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN
Received date: 2010-01-12
Revised date: 2011-08-25
Online published: 2012-07-20
Supported by
This research was supported by the National Natural Science Foundation of China (11071069 and 11171307), Natural Science Foundation of Hunan Province (09JJ6003) and Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924).
For p ∈ R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp(a, b) <T(a, b) < Lq(a, b) holds for all a, b > 0 and a ≠ b.
Key words： generalized logarithmic mean; Seifferts mean; power mean
CHU Yu-Ming , WANG Miao-Kun , WANG Gen-Di . THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1619 -1626 . DOI: 10.1016/S0252-9602(12)60128-3
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