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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convex analysis – Convexity defined by Karamata inequality – Mathematics Stack Exchange

Dividing by n gives Jensen’s inequaliity. Views Read Edit View history. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality. Let I be an interval of the real line and let f denote a real-valued, convex function defined on I. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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Inequalities of Jensen and Karamata

Convexity defined by Karamata inequality Ask Question. The finite form of Jensen’s inequality is a special case of this result. It generalizes the discrete form of Jensen’s inequality. Email Required, but never shown.

Retrieved from ” https: From Wikipedia, the free encyclopedia. By Karamata’s inequality 1 for the convex function f. In mathematicsKaramata’s inequality[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 interval of the real line.

However, then there is a strictly positive term on the right hand side of 7 and equality in 1 cannot hold.

Karamata’s inequality

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