Date: Apr 4, 2013 9:21 PM
Author: Brad Cooper
Subject: Is it possible to bound these functions?

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 want them to be.

\begin{equation*}
A\{f(x)\} = {\left[\int_0^1 \cos\left(\int_0^x f(t)dt\right) dx\right]}^2 +
{\left[\int_0^1 \sin\left(\int_0^x f(t)dt\right) dx\right]}^2
\end{equation*}

Given that $a \leq f(x) \leq b$, can it be shown that $A\{a\} \geq A\{f(x)\} \geq A\{b\}$ ?

Cheers,
Brad

PS Sorry about using LaTeX code. Is there a better way to show equations in Google Groups?