Univalence criteria for two integral operators
type: Item
instance of: scholarly article
title: Univalence criteria for two integral operators
zbMATH Open document ID: 1242.30013
DOI: 10.1155/2012/652858
author: Laura Stanciu
author: Daniel Breaz
published in: Abstract and Applied Analysis
publication date: 2012-04-03T00:00:00Z
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 6020989
zbMATH Keywords: univalence condition
zbMATH Keywords: integral operator
zbMATH Keywords: Schwarz lemma
Wikidata QID: Q58695816
reviewed by: Dmitri V. Prokhorov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/652858
OpenAlex ID: W2019508248
cites work: Convex and starlike criteria
cites work: Univalence of integral operators involving Bessel functions
cites work: Q3603342
cites work: Q4532975
cites work: Q4439096
cites work: Q4359776
cites work: Q5815016
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review text: Let \(A\) denote the class of functions \(f(z)=z+\sum_{n=2}^{\infty}a_nz^n\), \(|z|<1\). The authors prove two theorems and numerous corollaries giving univalence conditions for functions represented by the integral operators NEWLINE\[NEWLINEI(f_1,\dots,f_n;g_1,\dots,g_n)(z)= \left(\beta\int_0^zt^{\beta-1}\prod_{k=1}^n\left(\frac{f_k(t)}{t}\right)^{(a_k-1)/M_k}(g_k'(t))^{\gamma_k}dt\right)^{1/\beta}NEWLINE\]NEWLINE and NEWLINE\[NEWLINEJ(f_1,\dots,f_n;g_1,\dots,g_n)(z) = \left(\left(1+\sum_{k=1}^na_k\right)\int_0^z\prod_{k=1}^n(f_k(t))^{a_k}(g_k'(t))^{\gamma_k}dt\right)^{1/\left(1+\sum_{k=1}^na_k\right)},NEWLINE\]NEWLINE where, for \(k=1,\dots,n\), \(a_k,\gamma_k\in\mathbb C\), \(\beta\in\mathbb C\setminus\{0\}\), \(f_k,g_k\in A\) and \(M_k\geq1\).
description: scientific article; zbMATH DE number 6020989