On new classes of analytic functions with negative coefficients
type: Item
instance of: scholarly article
title: On new classes of analytic functions with negative coefficients
zbMATH Open document ID: 0582.30009
DOI: 10.1155/S0161171284000752
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46004
review text: The author considers the class \(K^*_ n\), \(n\in {\mathbb{N}}\cup \{0\}\), consisting of functions f(z) which satisfy in the unit disc \(| z| <1\), the conditions: \[ 1)\quad f(z)=z-\sum^{\infty}_{k=2}a_ kz^ k,\quad a_ k\geq 0,\quad and \] \[ 2)\quad Re\{D^{n+1} f(z)/D^ n f(z)\}>,\quad where\quad D^ n f(z)=f(z)*(z/(1-z)^{n+1}), \] (*) is the Hadamard product of power series. Coefficient inequalities, distortion and closure results are obtained.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 3931339
zbMATH Keywords: Ruscheweyh derivative
zbMATH Keywords: Hadamard product of power series
zbMATH Keywords: Coefficient inequalities
zbMATH Keywords: distortion
author: Shigeyoshi Owa
reviewed by: H. S. Al-Amiri
MaRDI profile type: Publication
OpenAlex ID: W1970885545
description: scientific article; zbMATH DE number 3931339