# 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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Dividing by n gives Jensen’s inequality. An explanation of Karamata’s inequality and majorization theory can be found here. Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions?

Consider the real numbers x 1.

MathOverflow works best with JavaScript enabled. Here majorization means that x 1. Email Required, but never shown.

CS1 French-language sources fr Articles containing proofs. Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

ECUACIONES DIFERENCIALES APLICADAS MURRAY R.SPIEGEL PDF

## Inequalities of Jensen and Karamata

Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality. Juanito 1, 4 Sign up or log in Sign up using Google. I am looking for a proof of weighted version of the inequality as following. 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.