someone1348, let $f$ be defined on an interval $I$ and suppose that there exists $M0$ and $\alpha0$ such that$$|f(y)-f(x)|\leq M|x-y|^\alpha$$for all $x,y\in I$. Is this the Lipschitz condition you're talking about?

Question

someone1348, let $f$ be defined on an interval $I$ and suppose that there exists $M>0$ and $\alpha>0$ such that$$|f(y)-f(x)|\leq M|x-y|^\alpha$$for all $x,y\in I$. Is this the Lipschitz condition you're talking about?

anonymous · Answer

Yep! look at my question, I have specified the function I need to prove lipschitz continuity for

jamesj · Answer

(for the record, the thing you've written down Across is usually called the uniform Lipschitz condition or Hölder continuity; when alpha = 1, then it's (vanilla, ordinary) Lipschitz.)