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A Simple Proof of Inequalities Related to Means
並列摘要
The purpose of this paper is to give a fairly elementary method to prove that the function (The equation is abbreviated), α≠0, 1, u(0)=I, u(1)=L, is strictly increasing, and to give a simple proof of the inequalities x＜H＜xy/I＜xy/L＜G＜L＜I＜A＜y, where 0＜x＜y and A, G, H, I, L are the arithmetic, the geometric, the harmonic, the identric and logarithmic means of x and y, respectively.
延伸閱讀
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