3 problems

Bohr-radius conjecture. If $a\in(a_1,1]$, then

Let $\mathcal{S}^{*}_{\wp}$ denote the class of cardioid starlike functions associated with $\psi(z)=1+ze^z$, and let $r_0$ denote the Bohr radius for this class. Bohr-radius conje…

Let $\mathcal{SL}^{*}$ denote the class of lemniscate starlike functions, associated with $\psi(z)=\sqrt{1+z}$. The Bohr-radius conjecture. The Bohr radius of $\mathcal{SL}^{*}$ is…