On a class of meromorphic \(p\)-valent starlike functions involving certain linear operators
type: Item
instance of: scholarly article
title: On a class of meromorphic \(p\)-valent starlike functions involving certain linear operators
zbMATH Open document ID: 1006.30013
DOI: 10.1155/S016117120220335X
author: Jin-Lin Liu
author: Shigeyoshi Owa
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-01-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49786
review text: Summary: Let \(\Sigma_{p}\) be the class of functions \(f(z)\) which are analytic in the punctured disk \({\mathbb E}^*= \{z\in {\mathbb C}: 0< |z|<1\}\). Applying the linear operator \(D^{n+p}\) defined by using the convolutions, the subclass \({\mathcal T}_{n+p}(\alpha)\) of \(\Sigma_{p}\) is considered. The object of the present paper is to prove that \({\mathcal T}_{n+p}(\alpha)\supset {\mathcal T}_{n+p-1}(\alpha)\). Since \({\mathcal T}_{0}(\alpha)\) is the class of meromorphic \(p\)-valent starlike functions of order \(\alpha\), all functions in \({\mathcal T}_{n+p-1}(\alpha)\) are meromorphic \(p\)-valent starlike in the open unit disk \({\mathbb E}\). Further properties preserving integrals and convolution conditions are also considered.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1852884
MaRDI profile type: Publication
OpenAlex ID: W2076384680
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description: scientific article; zbMATH DE number 1852884