What does it mean for a continuous function $ f $ on $ \mathbb{R} $ to be Hölder continuous with exponent $ \alpha $ at a point $ x_0 $ ?
I only now the global definition: A function $ f $ on $ \mathbb{R} $ is (globally) Hölder continuous with exponent $ \alpha $ if
$ \sup_{x \neq y} \frac{| f(x) - f(y) |}{ |x - y|^\alpha} < + \infty $
Thanks for the clarification!
Regards, Si