I am trying on problems from Bak and Newman's complex analysis. On the part of regarding Liouville's theorem, there were quite a number of problems concerns and an inequality and then ask you to prove that the complex-valued function is a linear one. An example is the following:
Suppose $f$ is entire and $|f(z)|\leq A+B|z|^{3/2}$ for constants $A,B$. Show that $f$ is a linear polynomial.
I hope someone can solve one of them for me. It will be helpful for me to understand problems of similar type once I understand this one!
Thanks in advance for answering.