# 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 inequalitiesâ€”those of Karamata, Schur and Muirheadâ€”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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### 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.

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.