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 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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Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold. Just as the Jensen inequality is used to define convex functions, can the Inequaliy inequality be used instead to define convex functions? Sign up or log in Sign up using Google.

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inequalities – Weighted version of the Karamata Inequality – MathOverflow

By clicking “Post Karamaha Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. An explanation of Karamata’s inequality and majorization theory can be found here. This is false by some stupid reasons. Convexity defined by Karamata inequality Ask Question. Here majorization means that x 1.

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IMOmath: Inequalities of Jensen and Karamata

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.

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Karamata’s inequality

We may assume that the numbers are in decreasing order as specified in 2. Sign up using Email and Password.