一个不等式的简单证明与推广(英文)

A Direct Proof and Extensions of An Inequality

中文关键词:  不等式  Hadamard不等式  Chebyshev不等式  推广

英文关键词:Inequality  Hadamard inequality  Chebyshev inequality  extensions.

中文摘要:

      本文讨论了一个引人注目而被广泛讨论的、与平均值有关的不等式.我们首先获得了它的完整形式,给出了一个非常简洁而能揭示问题本质的证明.由此我们自然地引出了它的最为一般的形式.同时,我们还指出文献中存在的一些谬误.

英文摘要:

      In this note, we discuss a well-known inequality which attracts considerable interest recently. We first obtain a full version of the inequality, then we give a concise and elementary proof which reveals its very essential. This naturally leads us to some more general extensions of it. Meanwhile, we point out some mistakes in the existing literature concerning the inequality.