Timeline for Lower bound for $ \sum_{i=1}^n x_i f(x_i)$ when $\sum_{i=1}^{n}x_i = K$

8 events

when toggle format	what		by	license	comment
Feb 25, 2022 at 15:11	history	edited	coudy	CC BY-SA 4.0	correct spelling
Jul 16, 2015 at 11:58	vote	accept	Anna maredric
Jul 5, 2015 at 2:47	answer	added	Apue		timeline score: 1
Jul 4, 2015 at 17:59	history	edited	YCor		edited tags
Jul 4, 2015 at 12:34	answer	added	Ofir Gorodetsky		timeline score: 4
Jul 4, 2015 at 11:58	comment	added	Ofir Gorodetsky		By Jensen, this is immediate for convex $f$: $\sum x_i f(x_i) = K \sum \frac{x_i}{K} f(x_i) \ge K f(\sum x_i^2 / K)$, and since $f$ is monotone increasing and by C-S $\sum x_i^2 / K \ge (\sum x_i)^2 /(nK) = K/n$, we're done.
Jul 4, 2015 at 11:46	review	First posts
Jul 4, 2015 at 11:56
Jul 4, 2015 at 11:43	history	asked	Anna maredric	CC BY-SA 3.0