KARAMATA INEQUALITY PDF

Shazshura inequalities — Weighted version of the Karamata Inequality — MathOverflow I am looking for a proof of weighted version of the inequality as following. Home Questions Tags Users Unanswered. MathOverflow works best with JavaScript enabled. Belgrade in French1: We may assume that the numbers are in decreasing order as specified in 2.

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Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions? Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold.

Sign up or log in Sign up using Google. However, then there is a strictly positive term on the right hand side of 7 and equality in 1 cannot karamats. Sign up using Email and Password. Sign up using Facebook. By using this site, you agree to the Terms of Use and Privacy Policy. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Inequalities of Jensen and Karamata Here majorization means that x 1. From Wikipedia, the free encyclopedia.

Home Questions Tags Users Unanswered. Mathematics Stack Exchange works best with JavaScript enabled. I am looking for a proof of weighted version of the inequality as following.

Post as a guest Name. Then x 1. MathOverflow works best with JavaScript enabled. Email Required, but never shown. Consider the real jnequality x 1. Let I be an interval of the real line and let f denote a real-valued, convex function defined on I. Convexity defined by Inequaliity inequality Ask Question.

We may assume that the numbers are in karamat order as specified in 2. Related Posts.

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KARAMATA INEQUALITY PDF

Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions? Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold. Sign up or log in Sign up using Google. However, then there is a strictly positive term on the right hand side of 7 and equality in 1 cannot karamats. Sign up using Email and Password.

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Life[ edit ] Jovan Karamata was born in Zagreb on February 1, into a family descended from merchants based in the city of Zemun , which was then in Austria-Hungary , and now in Serbia. In Lausanne , , he finished primary school oriented towards mathematics and sciences. In the same year he enrolled at the Engineering faculty of Belgrade University and, after several years moved to the Philosophy and Mathematicians sector, where he graduated in He spent the years — in Paris , as a fellow of the Rockefeller Foundation , and in he became Assistant for Mathematics at the Faculty of Philosophy of Belgrade University.

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