Univalent polynomials and fractional order differences of their coefficients
type: Item
instance of: scholarly article
title: Univalent polynomials and fractional order differences of their coefficients
zbMATH Open document ID: 1165.30003
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-04-29T00:00:00Z
review text: Let \(f(z)=z+\sum_{k=2}^{\infty}a_kz^k\) be analytic in the unit disk \(\mathbb D\). The author finds sufficient conditions on \(\{a_k\}\), \(k\geq2\), such that \(f\) is close-to-convex in \(\mathbb D\). Two theorems refer to polynomials \(f\) while four other theorems of the article treat infinite series. The proofs are based on straightforward estimates of corresponding sums.
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5549422
zbMATH Keywords: univalent functions
zbMATH Keywords: difference operator
zbMATH Keywords: zeros of polynomials
zbMATH Keywords: Gaussian hypergeometric functions
author: Anbhu Swaminathan
reviewed by: Dmitri V. Prokhorov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.11.054
OpenAlex ID: W2072194402
cites work: Q4351270
cites work: Coefficient regions for univalent polynomials of small degree
cites work: Zeros of polynomials and fractional differences of their coefficients
cites work: Coefficient Estimates for Univalent Functions
cites work: Two theorems on schlicht functions
cites work: Q3704135
cites work: Q5797046
cites work: Q3695546
cites work: Linear operators between classes of prestarlike functions
cites work: Q3695542
cites work: Inclusion theorems of convolution operators associated with normalized hypergeometric functions
DOI: 10.1016/J.JMAA.2008.11.054
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description: scientific article; zbMATH DE number 5549422