Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Karamata's Inequality

Revision as of 12:41, 12 September 2008 by 1=2 (talk | contribs) (New page: '''Karamata's Inequality''' states that if <math>(x_i)</math> majores <math>(y_i)</math> and <math>f</math> is a convex function, then <center><math>\sum_{i=1}^{n}f(x...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Karamata's Inequality states that if $(x_i)$ majores $(y_i)$ and $f$ is a convex function, then

$\sum_{i=1}^{n}f(x_i)\geq \sum_{i=1}^{n}f(y_i)$

Proof

Template:Incomplete

See also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Karamata%27s_Inequality&oldid=27901"