Date: Apr 5, 2013 6:41 AM
Author: Brad Cooper
Subject: Re: Is it possible to bound these functions?

Hi William,

The problem restated...

Define A{f(x)} as a mapping from the set of functions defined on the interval [0,1] to the Reals.

The functions are as "nice, smooth and integrable" as you may need them to be.

A{f(x)} = [ int cos(int f(t) t=0..x) x=0..1 ]^2 +
[ int sin(int f(t) t=0..x) x=0..1 ]^2

Given that a <= f(x) <= b, can it be shown that A{a} => A{f(x)} => A{b} ?