New question(s)

I am waiting for the response to my proof to this problem. (actually waiting kunny...)

Problems 1. Let $c$ be a real constant such that $\lim_{x\to 0} \frac{f(x)}{x}=c$. Find $f(x)$ which satisfies $f(x+y)\leq f(x)+f(y)$ for all real numbers $x,y$.

I can't solve the following but already get a solution from Dr. Kin Li.

Problem 2. Let $f$ be holomorphic on $\{z:|z|<1\}$ such that $|z|+|f(z)|\leq 1$, show that $f\equiv 0$.

我永遠都只係識喺一點附近整個圓俾佢=.=，以後都係睇 integrand 做人。