Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Is it possible to bound these functions?
Replies: 3   Last Post: Apr 5, 2013 10:15 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Brad Cooper

Posts: 167
Registered: 12/8/04
Is it possible to bound these functions?
Posted: Apr 4, 2013 9:21 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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?



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.