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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Levinson's inequality ： ウィキペディア英語版 Levinson's inequality In mathematics, Levinson's inequality is the following inequality, due to Norman Levinson, involving positive numbers. Let $a>0$ and let $f$ be a given function having a third derivative on the range $(0,2a)$, and such that :$f(x)\backslash geq\; 0$ for all $x\backslash in\; (0,2a)$. Suppose : $\backslash frac-f\backslash left(\backslash frac\backslash right)\backslash le\backslash frac-f\backslash left(\backslash frac\backslash right).$ The Ky Fan inequality is the special case of Levinson's inequality where :$p\_i=1,\backslash \; a=\backslash frac,$ and :$f(x)=\backslash log\; x.\; \backslash ,$ ==References== *Scott Lawrence and Daniel Segalman: ''A generalization of two inequalities involving means'', Proceedings of the American Mathematical Society. Vol 35 No. 1, September 1972. *Norman Levinson: ''Generalization of an inequality of Ky Fan'', Journal of Mathematical Analysis and Applications. Vol 8 (1964), 133–134. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Levinson's inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.