Open AccessMulti-dimensional Hadamard's inequalities
Author(s) -
Yin Chen
Publication year - 2012
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.43.2012.677
Subject(s) - mathematics , hadamard transform , convex function , regular polygon , convex body , combinatorics , ball (mathematics) , radius , convex set , function (biology) , pure mathematics , mathematical analysis , convex optimization , geometry , computer science , computer security , evolutionary biology , biology
In this paper, Hadamard's inequalities are extended to a convex function on a convex set in $R^2$ or $R^3$. In particular, it is proved that the average of convex function on a ball of radius $r$ is between the average of the function on the circle of radius r and that on the circle of $frac{2r}{3}