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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Karamata’s inequality

The finite form of Jensen’s inequality is a special case of this result. Convexity defined by Karamata inequality Ask Question. Post as a guest Name.

Weighted version of the Karamata Inequality Ask Question. By clicking “Post Your Answer”, you acknowledge that you inequalitu read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex. CS1 French-language sources fr Articles containing proofs. Email Required, but never shown.

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Let I be an karamara of the real line and let f denote a real-valued, convex function defined on I. Views Read Edit View history.

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

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. It generalizes the discrete form of Jensen’s inequality. Sign up using Facebook.

Retrieved from ” https: Consider the real numbers x 1. An explanation of Karamata’s inequality and majorization theory can be found here.

IMOmath: Inequalities of Jensen and Karamata

Mathematics Stack Exchange works best with JavaScript enabled. Sign up or log in Sign up using Google. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. However, then there is a strictly positive karamqta on the right hand side of 7 and equality in 1 cannot hold.

This is false by some stupid reasons. Post Your Answer Discard By clicking “Post Your 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. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality.

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Home Questions Tags Users Unanswered. Email Required, but never shown. I am looking for a proof of weighted version of the inequality as following. Here majorization means that x 1. We may assume that the numbers are in decreasing order as specified in 2.

Inequalities of Jensen and Karamata

Then x 1. Post as a guest Name. Sign up using Email and Password.

Post Your Answer Discard By clicking “Post Your 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. This page was last edited on 6 Octoberat MathOverflow works best with JavaScript enabled. By clicking “Post Your 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.

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