THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN  

作　　者：褚玉明 王淼坤 王根娣 

机构地区：[1]Department of Mathematics,Hunan City University,Yiyang 413000,China [2]College of Mathematics and Econometrics,Hunan University,Changsha 410082,China [3]Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China

出　　处：《Acta Mathematica Scientia》2012年第4期1619-1626,共8页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (11071069 and 11171307);Natural Science Foundation of Hunan Province(09JJ6003);Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)

摘　　要：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.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.

关 键 词：generalized logarithmic mean Seiffert＇s mean power mean 

分 类 号：O156[理学—数学]