Coefficient bounds and convolution properties for certain classes of close-to-convex functions
type: Item
instance of: scholarly article
title: Coefficient bounds and convolution properties for certain classes of close-to-convex functions
zbMATH Open document ID: 0965.30006
author: Jae Ho Choi
author: Toshiyuki Sugawa
author: Yong Chan Kim
published in: Proceedings of the Japan Academy. Series A
publication date: 2001-08-02T00:00:00Z
review text: In this paper, the authors introduce and study the class \(C(\varphi,\xi)\) of normalized close-to-convex functions which is defined by using the subordination for analytic functions \(\varphi\) and \(\xi\) on the unit disc. The authors derive the bounds of the quantity \(a_3-\mu a^2_2\) for the function \(f(z)=z+a_2 z^2+a_3z^3+ \dots\) in \(C(\varphi,\xi)\) in terms of \(\varphi\) and \(\xi\), where \(\mu\) is a real constant. They have shown that the class \(C(\varphi,\xi)\) is closed under the convolution operation by convex functions, or starlike functions of order 1/2 when \(\varphi\) and \(\xi\) satisfy some mild conditions.
reviewed by: Khalida Inayat Noor
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1538533
zbMATH Keywords: close-to-convex functions
zbMATH Keywords: convolution
zbMATH Keywords: convex functions
zbMATH Keywords: starlike functions
MaRDI profile type: Publication
full work available at URL: pjaa.76.95
OpenAlex ID: W2029401599
cites work: Q3660033
cites work: NORM ESTIMATES OF THE PRE-SCHWARZIAN DERIVATIVES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS
cites work: On the Fekete-Szego Problem for Close-to-Convex Functions
cites work: Q4035976
cites work: Q4840631
cites work: On the Coefficients of Subordinate Functions
cites work: Hadamard products of schlicht functions and the Polya-Schoenberg conjecture
DOI: 10.3792/PJAA.76.95
description: scientific article; zbMATH DE number 1538533