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Is it possible to bound these functions?
Posted:
Apr 4, 2013 9:21 PM


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?



