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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 Hermite–Hadamard inequality ： ウィキペディア英語版 Hermite–Hadamard inequality In mathematics, the Hermite–Hadamard inequality, named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard's inequality, states that if a function ƒ : () → R is convex, then the following chain of inequalities hold: : $f\backslash left(\; \backslash frac\backslash right)\; \backslash le\; \backslash frac\backslash int\_a^b\; f(x)\backslash ,dx\; \backslash le\; \backslash frac.$ == Retkes inequality: The concept of a sequence of iterated integrals == Suppose that −∞ < ''a'' < ''b'' < ∞, and let ''f'':(''b'' ) → ℝ be an integrable real function. Under the above conditions the following sequence of functions is called the sequence of iterated integrals of ''f'',where ''a'' ≤ ''s'' ≤ ''b''.: : $$ \begin F^(s) & := f(s), \\ F^(s) & := \int^s_a F^(u)du=\int^s_a f(u)du, \\ F^(s) & := \int^s_a F^(u)du=\int^s_a \left( \int^t_a f(u)du \right ) \, dt, \\ & \ \ \vdots \\ F^(s) & := \int^s_a F^(u) \, du, \\ & {}\ \ \vdots \end{align} 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「Hermite–Hadamard 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.