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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-.

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I am looking for a proof of weighted inquality of the inequality as following. Sign up using Email and Password. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Post as a guest Name. Here majorization means that x 1. From both sides of the inequality, but not from your conditions!

Inequalities of Jensen and Karamata

Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions? 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.

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Email Required, but never shown. We may assume that the numbers are in decreasing order as specified in 2. Post as a guest Name. Convexity defined by Karamata inequality Ask Question. Views Read Edit View history. By clicking “Post Your Answer”, you iaramata 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.

Karamata’s inequality – Wikipedia

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This is false karamaya some stupid reasons. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

IMOmath: Inequalities of Jensen and Karamata

Belgrade in French1: Post Your Answer Discard By inequalit “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 Mathematics Stack Exchange works best with JavaScript enabled. The finite form of Jensen’s inequality is a special case of this result. CS1 French-language sources fr Articles containing proofs. From Wikipedia, the free encyclopedia.

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Dividing by n gives Jensen’s inequality. It generalizes the discrete form of Jensen’s inequality. Sign up or log in Sign up using Google. By using this site, you agree to the Terms of Use and Privacy Policy. Home Questions Tags Users Unanswered. Sign up using Facebook.

Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex. Juanito 1, 4 Home Questions Tags Users Unanswered.

Let I be an interval of the real line and let f denote a real-valued, convex function defined on I. 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.

Email Required, but never shown. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality.