Radii of Starlikeness and Convexity of Some Entire Functions

Abstract

A normalized analytic function f is lemniscate starlike if the quantity $$zf'(z)/f(z)$$ lies in the region bounded by the right half of the lemniscate of Bernoulli $$|w^2-1|=1$$ . It is Janowski starlike if the quantity $$zf'(z)/f(z)$$ lies in the disk whose diametric end points are $$(1-A)/(1-B)$$ and $$(1+A)/(1+B)$$ for $$-1\le B<A\le 1$$ . The radii of lemniscate starlikeness and Janowski starlikeness have been determined for normalizations of q-Bessel functions, Bessel functions of first kind of order $$\nu $$ and Lommel functions of first kind. Corresponding convexity radii are also determined.