Multivalent functions defined by Ruscheweyh derivatives. II
type: Item
instance of: scholarly article
title: Multivalent functions defined by Ruscheweyh derivatives. II
zbMATH Open document ID: 0567.30013
author: Vinod Kumar
author: S. L. Shukla
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: [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 \(V_{n,p}(A,B)\).
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 3904919
zbMATH Keywords: Ruscheweyh derivative
zbMATH Keywords: p-valent
zbMATH Keywords: class preserving integral operators
reviewed by: David J. Hallenbeck
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3904919