Certain classes related to functions of bounded boundary rotation (Q1305309)

Let \(P[A,B](-1\leq B\leq A\leq 1)\) be defined as the class of all analytic functions \(p(z)\) in the open unit disc \(E\) of the complex plane which are subordinate to \((1+Az)(1+Bz)^{-1}\). Define \(f\in S^*[A,B]\) if and only if \([zf'(z)/f(z)]\in P[A,B]\). Denote by \(V_k[A,B,C,D]\) \((k\geq 2)\) the set of all analytic functions \(f(z)=z+ \sum^\infty_{n=2} a_nz^n\) in \(E\) with \(f'(z)\neq 0\) for which there exist \(s_1\in S^*[A,B]\) and \(s_2\in S^*[C,D]\) such that \(f'(z) =({s_1(z) \over z})^{{k\over 4}+{1\over 2}}({z\over s_2(z)})^{k/4-1/2}\). In this paper the author obtains distortion theorems, coefficient estimates and radius of convexity for \(V_k[A,B, C,D]\) and related families. The effect of a certain integral operator on this family is also studied.