Properties of close-to-convexity preserved by some integral operators
type: Item
instance of: scholarly article
title: Properties of close-to-convexity preserved by some integral operators
zbMATH Open document ID: 0581.30010
DOI: 10.1016/0022-247X(85)90260-4
author: Huda A. Alkhorasani
author: Khalida Inayat Noor
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The authors study operators of the form \[ f(z)=(1/\alpha)z^{1- (1/\alpha)}\int^{z}_{0}z^{(1/\alpha)-2}F(z)dz \] for \(F(z)=z+..\). and z in the open unit disk. They show, for example, that f(z) satisfies \[ Re\{zf'(z)/g(z)\}>\gamma \quad when\quad Re\{zF'(z)/G(z)\}>\beta,\quad Re\{zG'(z)/G(z)\}>\lambda \] and g(z) is the integral of G(z), above. Their work makes use of the methods of \textit{S. S. Miller} [Bull. Am. Math. Soc. 81, 79-81 (1975; Zbl 0302.30003)], and \textit{G. S. Sălăgean} [Lect. Notes Math. 1013, 362-372 (1983; Zbl 0531.30009)].
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 3929371
zbMATH Keywords: integral operator
zbMATH Keywords: convex starlike
zbMATH Keywords: close-to-convex
reviewed by: R.J.Libera
MaRDI profile type: Publication
cites work: Convex and Starlike Univalent Functions
cites work: Quasi-convex univalent functions
cites work: Q3885990
cites work: Some radius of convexity problems
cites work: Some Classes of Regular Univalent Functions
cites work: Differential inequalities and Carathéodory functions
cites work: Q3853876
cites work: Q4090611
cites work: Q3853877
full work available at URL: 0022-247x(85)90260-4
OpenAlex ID: W2076303121
description: scientific article; zbMATH DE number 3929371