Toader型平均的若干经典平均凸组合界

Some Classical Mean Convex Combination Bounds of Toader Type Mean

运用单调性L’Hospital法则,证明了两类Toader型平均关于其他若干经典平均的凸组合确界,进而给出了第二类完全椭圆积分的两个不等式.

Using the monotonicity L’Hospital rule,we present sharp bounds for the Toader type mean in terms of the convex combinations of several classical means.These results lead two best possible inequalities for the complete elliptic integrals of the second kind in some form.