Let $u$ be positive harmonic function in the unit disk such that $u(0)=\alpha$. Find upper and lower bound for number $u(3/4)$.
I tried to find an example, that is positive, harmonic( realvalued? and $\Delta u=0$) in the unit disk such that $u(0)=\alpha$. But this is closest I came; let $f(z)=x^2-y^2+\alpha$ then it satisfies all the conditions except that f(z)>0 is not true when $x<y$. So I ask if you can find example that satisfies the conditions. This assignment is contradictory, because $u>0$ but still you got $|z| \leq 1$. $|u|>0$ is of course trivially true, but I think in this case you want $u>0$.