Radius Constants for Analytic Functions with Fixed Second Coefficient

Abstract

Let $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ be analytic in the unit disk with second coefficient $a_2$ satisfying $|a_2|=2b$, $0\leq b\leq1$. Sharp radius of Janowski starlikeness and other radius constants are obtained when $|a_n|\leq cn+d$ ($c,d\geq0$) or $|a_n|\leq c/n$ ($c>0$) for $n\geq3$.