Schur-convex function: Difference between revisions

Revision as of 11:37, 5 October 2024

Revision as of 11:40, 5 October 2024

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<math>(x_i - x_j)\left(\frac{\partial f}{\partial x_i} - \frac{\partial f}{\partial x_j}\right) \ge 0 </math> for all <math>x \in \mathbb{R}^d</math>

holds for all {{nowrap|<math>1\le ≤ ''i'' , ''j'' ≤\le ''d''}}</math>.<ref>{{cite book|last1=E. Peajcariaac|first1=Josip|last2=L. Tong|first2=Y.|title=Convex Functions, Partial Orderings, and Statistical Applications|date=3 June 1992 |publisher=Academic Press|isbn=9780080925226|page=333}}</ref>

== Examples ==