# KARAMATA INEQUALITY PDF

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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 inequalities—those of Karamata, Schur and Muirhead—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-. Author: Dakazahn Faulkis Country: Pacific Islands Language: English (Spanish) Genre: Politics Published (Last): 13 August 2005 Pages: 239 PDF File Size: 10.83 Mb ePub File Size: 4.88 Mb ISBN: 871-7-24173-725-1 Downloads: 75159 Price: Free* [*Free Regsitration Required] Uploader: Kigasho ## Inequalities of Jensen and Karamata

### Karamata’s inequality – Wikipedia

Weighted version of the Karamata Inequality Ask Question. Then x 1. An explanation of Karamata’s inequality and majorization theory can be found here. Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold.

## Karamata’s inequality

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Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex. Home Questions Tags Users Unanswered. ### convex analysis – Convexity defined by Karamata inequality – Mathematics Stack Exchange

Just as the Jensen karmaata is used to define convex functions, can the Karamata inequality be used instead to define convex functions? We may assume that the numbers are in decreasing order as specified in 2. This is false by some stupid reasons. It generalizes the discrete form of Jensen’s inequality. Let I be an interval of the real line and let f denote a real-valued, convex function defined on I.

Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality. Retrieved from ” https: In mathematicsKaramata’s inequality named after Jovan Karamata 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.

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