# Math Help - bounded anlaytic function.

1. ## bounded anlaytic function.

Let $f$ be analytic in the open disk $D(z_{0},R)$. Let $r< R\hat$ and $\gamma_{r}$ be the anticlockwise oreinted circle of radius $r$ centered at $z_{0}$.

Let $w \in$ tr $\gamma_{r}$.

Does it follow that $f(w)$ is bounded on tr $\gamma_{r}$?

Thanks

2. ## Re: bounded anlaytic function.

what is "tr"?

3. ## Re: bounded anlaytic function.

sory, it denotes the trace of $\gamma_{r}$. i.e. the image of the map/contour $\gamma_{r}$.

4. ## Re: bounded anlaytic function.

A circle is compact so any continuous function on it is bounded.