Radius Constants for Analytic Functions with Fixed Second Coefficient

Abstract EN

Let f(z) = z +∑n=2∞anzn be analytic in the unit disk with the second coefficient a2 satisfying a2 = 2b, 0≤b≤1.

Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies an≤cn+d (c,d≥0) or an≤c/n (c>0 and n≥3).

Other radius constants are also obtained for these functions, and connections with earlier results are made.