On a certain condition for p-valently starlikeness
type: Item
instance of: scholarly article
title: On a certain condition for p-valently starlikeness
zbMATH Open document ID: 0668.30020
author: Mamoru Nunokawa
author: Shigeyoshi Owa
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: Let A(p) be the class of functions of the form \(f(z)=z^ p+\sum^{\infty}_{n=p+1}a_ nz^ n\) \((p=1,2,...)\) which are analytic in \(\Delta =(z: | z| <1)\). A function \(f\in A(p)\) is said to be p-valently starlike if and only if it satisfies the condition \(Re zf'(z)/f(z)>0(z\in \Delta).\) The author's main theorem gives conditions which imply \(| \arg zf'(z)/f(z)| <(\pi /2)\alpha (0<\alpha \leq 1)\) for \(z\in \Delta\). This implies that such a function is p-valently starlike. One of the two assumptions made by the authors is that \(| \arg f'(z)/z^{p-1}| <(\pi /2)\alpha\) for z in \(\Delta\). The other assumption deals with the imaginary part of \(f'(z)/z^{p-1}\) and we do not give it here.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 4093840
zbMATH Keywords: p-valently starlike
reviewed by: David J. Hallenbeck
MaRDI profile type: Publication
full work available at URL: pjaa.64.331
OpenAlex ID: W2071608409
cites work: On the theory of multivalent functions
cites work: Q3485136
cites work: Coefficient conditions for starlike functions
DOI: 10.3792/PJAA.64.331
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description: scientific article; zbMATH DE number 4093840