On certain classes of meromorphically \(p\)-valent starlike functions
type: Item
instance of: scholarly article
title: On certain classes of meromorphically \(p\)-valent starlike functions
zbMATH Open document ID: 0804.30011
DOI: 10.1016/0893-9659(94)90107-4
author: Nak Eun Cho
author: Shigeyoshi Owa
published in: Applied Mathematics Letters
publication date: 1994-08-07T00:00:00Z
review text: Let \(\sum_ p\) denote the class of functions \(f(z) = \sum^ \infty_{k = - p} a_{k + p - 1} z^ k\) with \((a_{-1}=1)\) which are analytic for \(0<| z |<1\) and define \(D^{n+p-1} f(z) = z^{-p} (1-z)^{-n- p}*f(z)\) where \(*\) indicates the Hadamard product. The authors consider the classes \(M_{n+p-1} (\alpha)\) for which \[ \text{Re}\{z(D^{n+p- 1}f(z))'/ D^{n+p-1} f(z)\}<-\alpha \] in this annulus where \(0 \leq \alpha<p\). They then prove that these classes are nested, \(M_{n + p} (\alpha) \subset M_{n+p-1} (\alpha)\).
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 612154
zbMATH Keywords: Hadamard product
reviewed by: James A. Hummel
MaRDI profile type: Publication
full work available at URL: 0893-9659(94)90107-4
OpenAlex ID: W4238213154
cites work: Certain integrals for classes of p-valent meromorphic functions
cites work: Functions Starlike and Convex of Order α
cites work: Q4125074
cites work: Q4740137
cites work: New Criteria for Univalent Functions
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description: scientific article; zbMATH DE number 612154