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-.

Author: Galkree Gunos
Country: Timor Leste
Language: English (Spanish)
Genre: Politics
Published (Last): 2 November 2010
Pages: 475
PDF File Size: 7.58 Mb
ePub File Size: 20.17 Mb
ISBN: 941-7-89756-985-9
Downloads: 45181
Price: Free* [*Free Regsitration Required]
Uploader: Momuro

Sign up or log in Sign up using Google. 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. Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex. We may assume that the numbers are in decreasing order as specified in 2. 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.

  CIRCULAR STATISTICS IN BIOLOGY BATSCHELET PDF

Home Questions Tags Users Unanswered. It generalizes the discrete form of Jensen’s inequality. 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.

Email Required, but never shown. Sign up using Facebook. From both sides of the inequality, but not from your conditions! From Wikipedia, the free encyclopedia. Just as the Jensen inequality is used to define convex functions, can the Karamata inequality be used instead to define convex functions?

Sign up or log in Sign up using Google. Views Read Edit View history. By Karamata’s inequality 1 for the convex function f.

Then x 1. Juanito 1, 4 Let I be an interval of the real line and let f denote a real-valued, convex function defined on I. However, then there is a strictly positive term on the right hand side of 7 karxmata equality in 1 cannot hold.

Here majorization means that x 1. Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality.

inequalities – Weighted version of the Karamata Inequality – MathOverflow

Sign up using Facebook. Weighted version of the Karamata Inequality Ask Question.

Retrieved from ” https: MathOverflow works best with JavaScript enabled. Dividing by n gives Jensen’s inequality.

  HERMANN HESSE NARCIS A GOLDMUND PDF

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

I am looking for a proof of weighted version of the inequality as following. Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold. The finite form of Jensen’s inequality is a special case of this result. Home Questions Tags Users Unanswered. Post as a guest Name.

Inequalities of Jensen and Karamata

Sign up using Email and Password. CS1 French-language sources fr Articles containing proofs.

This page was last edited on 6 October ineqjality, at Mathematics Stack Exchange works best with JavaScript enabled. 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. By using this site, you agree to the Terms of Use and Privacy Policy.