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摘要
We prove that the inequality TQ(a,b) > L-p(a,b) holds for all a,b > 0 with a not equal b if and only if p <= 3/2, where TQ(a,b) = (2/pi) integral(pi/2)(0) a(cos2 theta)bsin(2 theta)d theta, L-p(a,b) - inverted right perpendicular(bp - ap)/(p(b - a))inverted left perpendicular(1/p) (p not equal 0), and L-0(a,b) = root ab are, respectively, the Toader-Qi and p-order logarithmic means of a and b. As applications, we find two fine inequalities chains for certain bivariate means.
- 出版日期2016
- 单位湖南城市学院
