Classes of univalent integral operators
type: Item
instance of: scholarly article
title: Classes of univalent integral operators
zbMATH Open document ID: 0729.30011
DOI: 10.1016/0022-247X(91)90141-L
author: Sanford S. Miller
author: Petru T. Mocanu
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: If \(f(z)=z+a_ 2z^ 2+..\). is analytic in the disk U, then \[ I(f)(z)=[\frac{\beta +\gamma}{z^{\gamma}\Phi (z)}\int^{z}_{0}f^{\alpha}(t)\phi (t)t^{\delta - 1}dt]^{1/\beta}=z+b_ 2z^ 2+... \] is univalent (and starlike or convex) for suitable choices of the analytic functions \(\phi\) (z) and \(\Phi\) (z) and parameters \(\alpha\), \(\beta\), \(\gamma\) and \(\delta\). In various forms this operator has been studied by many investigators as is well-documented in the authors' presentation. The purpose of the paper is to allow the parameters \(\alpha\), \(\beta\), \(\gamma\) and \(\delta\) to be complex and to admit greater variety in the choices of f(z). The authors make clever use of subordination techniques developed here which follow from their earlier papers on integral operators.
reviewed by: R.J.Libera
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 4204743
zbMATH Keywords: integral transform
zbMATH Keywords: closed-to-convex
zbMATH Keywords: starlike
zbMATH Keywords: subordination
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4204743