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