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 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-.

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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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Sign up using Email and Password. From Wikipedia, the free encyclopedia. Post as a guest Name. Consider the real numbers x 1. Sign up using Facebook. Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex.

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Inequalities of Jensen and Karamata

By clicking “Post Your Laramata, 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. However, then there is a strictly positive term on the right hand side of 7 and equality in 1 cannot hold.

Dividing by n gives Jensen’s inequality. By using this site, you agree to the Terms of Use and Privacy Policy. Home Questions Tags Users Unanswered. Then x 1. Sign up or log in Sign up using Google. Convexity defined by Karamata inequality Ask Question. Sign up or log in Sign up using Google.

From both sides of the inequality, but not from your conditions! It generalizes the discrete form of Jensen’s inequality. Views Karxmata Edit View history. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality. This page was last edited on 6 Octoberat Belgrade in French1: I am looking for a proof of weighted version of the inequality as following.

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inequalities – Weighted version of the Karamata Inequality – MathOverflow

Let I be an interval of the real line and let f denote a real-valued, convex function defined on I. CS1 French-language sources fr Articles containing proofs. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie karammataand that your continued use of the website is subject to these policies.

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Karamata’s inequality

An explanation of Karamata’s inequality and majorization theory can be found here. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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Sign up using Email and Password. Here majorization means that x 1.