Relative Convexity and Its Applications
Classical Analysis and ODEs
2014-10-03 v2
Abstract
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under attention. Based on this fact, an extension of the Hardy-Littlewood-P\'olya theorem of majorization is proved and new insight is given into the problem of risk aversion in mathematical finance.
Keywords
Cite
@article{arxiv.1409.2772,
title = {Relative Convexity and Its Applications},
author = {Constantin P. Niculescu and Ionel Roventa},
journal= {arXiv preprint arXiv:1409.2772},
year = {2014}
}
Comments
to appear in Aequationes Mathematicae