数学研究与评论
數學研究與評論
수학연구여평론
JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION
2004年
4期
649-652
,共4页
不等式%Hadamard不等式%Chebyshev不等式%推广
不等式%Hadamard不等式%Chebyshev不等式%推廣
불등식%Hadamard불등식%Chebyshev불등식%추엄
Inequality%Hadamard inequality%Chebyshev inequality%extensions
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.
本文討論瞭一箇引人註目而被廣汎討論的、與平均值有關的不等式.我們首先穫得瞭它的完整形式,給齣瞭一箇非常簡潔而能揭示問題本質的證明.由此我們自然地引齣瞭它的最為一般的形式.同時,我們還指齣文獻中存在的一些謬誤.
본문토론료일개인인주목이피엄범토론적、여평균치유관적불등식.아문수선획득료타적완정형식,급출료일개비상간길이능게시문제본질적증명.유차아문자연지인출료타적최위일반적형식.동시,아문환지출문헌중존재적일사류오.
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.
