On radii of convexity and starlikeness of some classes of analytic functions (Q1187078)

Let \(P(A,B)\) denote the class of analytic functions in the unit disc which are subordinate to \((1+Az)/(1+Bz)\) for some \(A\) and \(B\) with \(-1\leq B<A\leq 1\). \(C(A,B)\) and \(S^*(A,B)\) represent classes of analytic functions \(f\) such that \((zf'(z))'/f(z)\) and \(zf'(z)/f(z)\) belong to \(P(A,B)\) respectively. The author obtains the best possible radius \(r\) such that \[ f\in S^*(A,B)\Rightarrow f\in C\left({1-A\over 1- B}\right)\text{ for } | z|<r. \] A few other results of similar nature are also obtained.