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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Here majorization means that x 1.

Inequalities of Jensen and Karamata

Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex. From both sides of the inequality, but not from your conditions! Belgrade in French1: Email Required, but never shown.

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. Weighted version of the Karamata Inequality Ask Question.

I am looking for a proof of weighted version of the inequality as following. Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions?

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Karamata’s inequality – Wikipedia

Juanito 1, 4 Post as a guest Name. From Wikipedia, the free encyclopedia. Post as a guest Name. Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold.

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Convexity defined by Karamata inequality Ask Question. Then x 1.

Karamata’s inequality

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 policyand that your continued use of the website is subject to these policies.

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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.

Email Required, but never shown. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality. Sign up using Facebook. An explanation of Karamata’s inequality and majorization theory can be found here.

Sign up or log in Sign up using Google. We may assume that the numbers are in decreasing order as ineqiality in 2. This is false by some stupid reasons. Home Questions Tags Users Unanswered.