Radius Constants for Analytic Functions with Fixed Second Coefficient

Abstract

Letf(z) = z +∑n=2∞anznbe analytic in the unit disk with the second coefficienta2satisfyinga2 = 2b,0≤b≤1. Sharp radius of Janowski starlikeness is obtained for functionsfwhosenth coefficient satisfiesan≤cn+d  (c,d≥0)oran≤c/n  (c>0  and  n≥3). Other radius constants are also obtained for these functions, and connections with earlier results are made.