# 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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## Inequalities of Jensen and Karamata

Dividing by n gives Jensen’s inequality.

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. This is false by some stupid reasons.

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

By clicking “Post Your Answer”, you acknowledge that you have read our updated terms inequaliyt serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. An explanation of Karamata’s inequality and majorization theory can be found here. The finite form of Jensen’s inequality is a special case of this result.

Email Required, but never shown. 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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