调和平均、对数平均和反调和平均间的最佳不等式

An Optimal Inequality Between Harmonic,Logarithmic and Contraharmonic Means

获得了使得不等式Cα(a,b)H1-α(a,b)<L(a,b)<βC(a,b)+(1-β)H(a,b)对所有a,b>0且a≠b成立的α和β的最佳值,其中C(a,b)、H(a,b)、L(a,b)分别为a,b的反调和平均、调和平均和对数平均.

The best possible α and β were presented such that the double inequality Ca（a,b）H1-a（a,b）〈L（a,b）〈βC（a,b）＋（1-β）H（a,b） held for all a,b 〉 Owith a≠b, where C（a,b） , H（a,b） , L（a, b） denoted the contraharmonie, harmonic and logarithmic means of a and b, respectively.