- #1
Perisona
- 2
- 0
Hello,
The function in question has the following properties:
1. Is monotonically increasing
2. Is concave downwards
3. f(0) =0
I was trying to find a relation between sum(f(x_i)) and f(sum(x_i)) i=1 to i=n and all x_i positive.
I tried a few things, including this:
nx>=x
f'(nx)<=f'(x)
integrating 0 to x
(1/n)f(nx)<=f(x)
taking sigma
sum((1/n)f(nx))<=sum(f(x))
i tried using this along with jensen's inequality but couldn't draw any conclusions. Any help would be greatly appreciated.
The function in question has the following properties:
1. Is monotonically increasing
2. Is concave downwards
3. f(0) =0
I was trying to find a relation between sum(f(x_i)) and f(sum(x_i)) i=1 to i=n and all x_i positive.
I tried a few things, including this:
nx>=x
f'(nx)<=f'(x)
integrating 0 to x
(1/n)f(nx)<=f(x)
taking sigma
sum((1/n)f(nx))<=sum(f(x))
i tried using this along with jensen's inequality but couldn't draw any conclusions. Any help would be greatly appreciated.