S*(φ) and C(φ)-Radii for Some Special Functions

The radius problem explaining the geometric properties of the normalized forms of the special functions has been of special interest among the Geometric function theories. In this paper, we consider the Ma-Minda classes of analytic functions S* (phi) := {f is an element of A : (zf'(z)/f(z))) < phi(z)} and Co(phi) : {f is an element of A : (1 + zf ''(z)/f'(z)) < phi(z)} defined on the unit disk D and show that the classes S*(1+alpha z) and C(1 + az), 0<alpha <= 1 solve the problem of finding the sharp S*(phi)-radii and C(phi)-radii for some normalized special functions, whenever phi(-) = 1 - a. Radius of strongly starlikeness is also considered.