Hi,
I would like to show that a continuous map
a,b)\to \mathbb{R}" alt="f
a,b)\to \mathbb{R}" /> which has the property that
for
satisfies
for some constants
.
I can prove it on the closed interval [0,1]: in this case it suffices to show
with
. I prove it holds on the dyadic rationals of the form
by an induction argument, and extending to the closed interval by continuity.
BUT my argument needs the endpoints of the interval: I am progressively subdividing;
, etc, and I cannot see how to prove it on an
open interval.
Many thanks