Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $ \Omega $ be an open and bounded subset of $ \mathbb{R^n} $, and let $ f:\Omega \to \mathbb{R} $ be a continuous function. I'm looking for some (preferably, minimal) conditions on $ f $ under which, for some $ M \ge 0 $,

$ \frac{diam(f(B(x,2r)))}{diam(f(B(x,r)))} \le M $

for all $ B(x,2r) \subseteq \Omega $ when $ diam(f(B(x,r))) > 0 $.

Any help would be greatly appreciated.

Thanks.

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.