4 problems

Let $f(z)=z+a_{2}z^{2}+a_{3}z^{3}+\cdots$ belong to the class $\mathcal{S}_{G}^{\ast}$. The coefficients $a_n$ are the Taylor coefficients of $f$. Coefficient-bound conjecture. The…

Kumar–Gangania conjecture. If $f\in\mathcal{S}_{\wp}^{*}$, then the sharp bound is

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…