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In mathematics, Karamata's inequality, named after Jovan Karamata, also known as the majorization inequality, is a theorem in elementary algebra for convex and concave real-valued functions, defined on an interval of the real line. It generalizes the discrete form of Jensen's inequality. ==Statement of the inequality== Let be an interval of the real line and let denote a real-valued, convex function defined on . If and are numbers in such that majorizes , then Here majorization means that and, after relabeling the numbers and , respectively, in decreasing order, i.e., we have If is a strictly convex function, then the inequality () holds with equality if and only if, after relabeling according to (), we have for all }. 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「Karamata's inequality」の詳細全文を読む スポンサード リンク
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