
Re: AskanAnalysis problem
Posted:
Apr 24, 2013 10:06 PM


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 AskanAlgebraist forum at at.yorku.ca/topology to give your simple disproof directly to the primary source.

