Multivalent functions defined by Ruscheweyh derivatives. II
[For part I see the paper reviewed above.] Let \(V_{n,p}(A,B)\) denote the class of functions \(f(z)=z^ p+\sum^{\infty}_{k=1}a_{p+k}z^{p+k}\) which are analytic in the unit disc U and satisfy the condition \(((D^{n+p-1}f(z))^{(')}/z^{p- 1})\prec p(1+Az)/(1+Bz),\) \(z\in U\) where \(-1\leq B<A\leq 1\), n is any integer such that \(n>-p\) and \(D^{n+p-1}f(z)\) denote the \((n+p-1)th\) order Ruscheweyh derivative of f(z). The authors show that the functions in \(V_{n,p}(A,B)\) are p-valent. They also obtain class preserving integral operators, sharp coefficient estimates and a closure theorem for a class \(V_{n,p}(A,B)\).
scientific article; zbMATH DE number 3904919