Timeline for Generalization of Popoviciu's inequality
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 25, 2016 at 14:02 | comment | added | Oai Thanh Đào | Dear Dr. @darijgrinberg I give a conjecture generalization of Popociviu's inequality as following, and I am looking for a proof. Let $f(x)$ is a real continuous function that is strictly convex on $[m, M]$, let $m \le x_1 \le x_2 \le x_3 \le...\le x_n \le M$ then show that: $nf\left(\frac{x_1+\cdots+x_n}{n}\right)+f(x_1)+\cdots+f(x_n) \ge 2f(\frac{x_1+x_2}{2})+....+2f(\frac{x_{n-1}+x_n}{2})+2f(\frac{x_{n}+x_1}{2}) $ Equality holds if only if $x_1=x_2=\cdots=x_n$ | |
| S Jun 29, 2015 at 0:50 | history | suggested | Peter Mortensen | CC BY-SA 3.0 |
Copy edited.
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| Jun 29, 2015 at 0:13 | review | Suggested edits | |||
| S Jun 29, 2015 at 0:50 | |||||
| Jun 28, 2015 at 19:51 | answer | added | Gjergji Zaimi | timeline score: 10 | |
| Jun 28, 2015 at 19:26 | comment | added | darij grinberg | There are some analogues of Popoviciu's inequality which do have a more interesting structure than just values and their average on the LHS. See artofproblemsolving.com/community/c6h98832p557719 | |
| Jun 28, 2015 at 19:24 | comment | added | darij grinberg | I fear this is not true. See my post at artofproblemsolving.com/community/c6h244828p1348667 | |
| Jun 28, 2015 at 19:16 | comment | added | Joseph O'Rourke | It might be worth numerical calculations to verify that it seems to be true... | |
| Jun 28, 2015 at 18:19 | history | asked | Marek Adamczyk | CC BY-SA 3.0 |