Radius Constants for Analytic Functions with Fixed Second Coefficient

Abstract

Let $f(z)=z+{\sum }_{n=2}^{\infty }{a}_n{z}^n$ be analytic in the unit disk with second coefficient $a_2$ satisfying $|a_2|=2b$, $0\le b\le 1$. Sharp radius of Janowski starlikeness and other radius constants are obtained when $|a_n|\le cn+d$ ($c,d\ge 0$) or $|a_n|\le c/n$ ($c>0$) for $n\ge 3$.