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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Email Required, but never shown. 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. Home Questions Tags Users Unanswered. Weighted version of the Karamata Inequality Ask Question. Mathematics Stack Exchange works best with JavaScript enabled.

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

Home Questions Tags Users Unanswered. From both sides of the inequality, but not from your conditions! The finite form of Jensen’s inequality is a special case of this result.

Hence, if a function satisfies Karamata’s inequality, it satisfies also Ineequality inequality and, thus, is convex. Post as a guest Name.

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Karamata’s inequality

We may assume that the numbers are in decreasing order as specified in 2. By Karamata’s inequality 1 for the convex function f. Kxramata up or log in Sign up using Google. Sign up using Facebook. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality.

Consider the real numbers x 1. This page was last edited on 6 Octoberat Views Read Edit View history.

inequalities – Weighted version of the Karamata Inequality – MathOverflow

Email Required, but never inequzlity. However, then there is a strictly positive term on the right hand side of 7 and equality in 1 cannot hold. Here majorization means that x 1.

Sign up using Email and Password. Dividing by n gives Jensen’s inequality.

Then x 1. Belgrade in French1: It generalizes the discrete form of Jensen’s inequality. MathOverflow works best with JavaScript enabled. Retrieved from ” https: Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions?

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

CS1 French-language sources fr Articles containing proofs. Convexity defined by Karamata inequality Ask Question.

I am looking for a proof of weighted karwmata of the inequality as following. An kraamata of Karamata’s inequality and majorization theory can be found here. 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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By using our site, you acknowledge that you have read and understand our Cookie KaramatqPrivacy Policyand our Terms of Service. This is false by some stupid reasons. 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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Inequalities of Jensen and Karamata

From Wikipedia, the free encyclopedia. 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.

Juanito 1, 4 By clicking “Post Inequaliity 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 inequakity these policies.

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. Sign karamatta using Email and Password.