摘要
设G(a,b),A(a,b)和L(a,b)分别是两不相等正数a和b的几何平均、算术平均和对数平均.本文得以下两重要结论①L<pG+(1-p)A成立的充要条件为-∞<p≤23;②GpA1-p<L成立的充要条件为23≤p<+∞.
Abstract Assume a and b to be two different positive number, let G(a,b), A(a,b) and L(a,b) be the unweighted geometric, arithmetic and logarithmic means of a and b, then two inequalities were obtained as follows:① L<pG+(1-p)A holds when and only when -∞<p≤23.② GpA1-p<L holds when and only when 23≤p<+∞.
出处
《工科数学》
1998年第2期150-154,共5页
Journal of Mathematics For Technology