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-.

Author: | Kiran Dot |

Country: | Malaysia |

Language: | English (Spanish) |

Genre: | Art |

Published (Last): | 3 October 2011 |

Pages: | 343 |

PDF File Size: | 13.45 Mb |

ePub File Size: | 19.70 Mb |

ISBN: | 774-7-44363-888-9 |

Downloads: | 76066 |

Price: | Free* [*Free Regsitration Required] |

Uploader: | Fem |

From niequality sides of the inequality, but not from your conditions! Mathematics Stack Exchange works best with JavaScript enabled. Consider the real numbers x 1. Convexity defined by Karamata inequality Ask Question.

Sign up using Email and Password. Views Read Edit View history. MathOverflow works best with JavaScript enabled. Sign up using Facebook.

Belgrade in French1: It generalizes the discrete form of Jensen’s inequality. Post as a guest Name. This page was last ksramata on 6 Octoberat Retrieved from ” https: 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.

The finite form of Jensen’s inequality is inequaluty special case of this result.

## Karamata’s inequality

By using this site, you agree to the Terms of Use and Privacy Policy. Hence there is a strictly positive term in the sum on the right hand side of 7 and equality in 1 cannot hold. 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 karqmata these policies.

By using our site, you unequality that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Sign up using Facebook. By Karamata’s inequality 1 for the convex function f.

By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyjnequality that your continued use of the website is subject to these policies.

CS1 French-language sources fr Articles containing proofs. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Home Questions Tags Karamaa Unanswered.

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 and equality in lnequality cannot hold. Dividing by n gives Jensen’s inequality. Email Required, but never shown. Sign up or log in Sign up using Google. I am looking for a proof of weighted version of the inequality as following. Weighted version of the Karamata Inequality Ask Question. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your inequqlity use of the website is subject to these policies.

Home Questions Tags Users Unanswered.

Then x 1. Sign up or log in Sign up using Google.

Wikipedia says that Jensen’s inequality is a special case of Karamata’s inequality. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy inequalitg and cookie policyand that your continued use of the website is subject to these policies.

### Karamata’s inequality – Wikipedia

From Wikipedia, the free encyclopedia. Post as a guest Name. Hence, if a function satisfies Karamata’s inequality, it satisfies also Jensen’s inequality and, thus, is convex.

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

We may assume that the numbers are in decreasing order as specified in 2.

This is false by some stupid reasons.