## KARAMATA INEQUALITY PDF

Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality . Hence, if a function satisfies Karamata’s inequality, it satisfies. PDF | Three classical general inequalitiesâ€”those of Karamata, Schur and Muirheadâ€”are proved in this article. They can be used in proving other inequali- ties. jorization inequality where the majorization condition is replaced by a more The inequality presented in the article is a consequence of Karamata’s majoriza-.

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### Karamata’s inequality – Wikipedia

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## Karamata’s inequality

In mathematicsKaramata’s inequality inequalityy, [1] named after Jovan Karamata[2] also known as the majorization inequalityis a theorem in elementary algebra for convex and concave real-valued functions, defined on an jaramata of the real line.

Views Read Edit View history. Then x 1. By Karamata’s inequality 1 for the convex function f. Email Required, but never shown. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality.

Hence there karamatz a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold. Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex.