most recent 30 from http://mathoverflow.net 2013-05-24T10:28:02Z http://mathoverflow.net/feeds/user/16916 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72022/global-index-of-convexity-concavity-of-a-function VitoshKa 2011-08-03T18:27:23Z 2011-08-04T09:03:43Z

<p>We are looking for a global index of the convexity/concavity of a function. </p> <p>For concreteness, how can I formalize the intuitive notion that a function $f$ is more convex than $g$ where $f,g:[0,1]\rightarrow \mathbb{R}$ are both increasing. </p> <p>The only index which I am aware of and could be used for this purpose is the <a href="http://en.wikipedia.org/wiki/Gini_coefficient" rel="nofollow">Gini</a> coefficient.</p> <p>Thanks.</p>

http://mathoverflow.net/questions/72022/global-index-of-convexity-concavity-of-a-function VitoshKa 2011-08-04T11:27:43Z 2011-08-04T11:27:43Z

Thanks @Peter, that's helpful, but it's only about partial convex order. No global index as we need.

http://mathoverflow.net/questions/72022/global-index-of-convexity-concavity-of-a-function VitoshKa 2011-08-04T09:08:50Z 2011-08-04T09:08:50Z

@quid, @Spencer Sorry for not being precise, I modified the request. Indeed, I am looking for a general answer and hint to literature or fields where such indexes where defined.