Page 141, Question 3:
Let $G=\{z:|\operatorname{Im} z| < \pi/2\}$ and suppose $f:G\rightarrow C$ and $\limsup|f(z)| \leq M$ on $w$ in the boundary of $G$. Also, suppose $A < \infty$ and $a < 1$ can be found such that $|f(z)| < \exp[A \exp(a|\operatorname{Re} z|)]$ for all $z$ in $G$. Show that $|f(z)|\leqslant M$ for all $z$ in $G$.
Thanks in advance.