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Topic: Ask-an-Analysis problem
Replies: 10   Last Post: Apr 25, 2013 1:01 PM

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William Elliot

Posts: 1,532
Registered: 1/8/12
Re: Ask-an-Analysis problem
Posted: Apr 24, 2013 10:06 PM
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On Wed, 24 Apr 2013, dullrich@sprynet.com wrote:

> >Assume for f:[0,1] -> R that there's some c /= 0,1 with
> >for all x in [0,1/2], f(x) = c.f(2x).
> >
> >Show there's some k with for all x in [0,1], f(x) = kx.


Whoops, indeed a hypothesis was omitted.

Assume for continuous f:[0,1] -> R here's some c /= 0,1 with
for all x in [0,1/2], f(x) = c.f(2x).

Show there's some k with for all x in [0,1], f(x) = kx.

> Forget what I said this morning. The question was either
> totally garbled or totally stupid to begin with.
> f(x) = x^2 is a counterexample.


You could go to Ask-an-Algebraist forum at
at.yorku.ca/topology
to give your simple disproof directly to the primary source.





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