Fekete-Szegő problems for quasi-subordination classes
type: Item
instance of: scholarly article
title: Fekete-Szegő problems for quasi-subordination classes
zbMATH Open document ID: 1267.30047
DOI: 10.1155/2012/192956
author: Maisarah Haji Mohd
author: Maslina Darus
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: In 1970 \textit{M. Robertson} [Bull. Am. Math. Soc. 76, 1--9 (1970; Zbl 0191.09101)] introduced the notion of quasi-subordination. The function \(f\) is quasi-subordinated to \(g\), written as \(f \prec_q q\), if there exist the analytic functions \(\varphi\) and \(\omega\) satisfying \(|\varphi(z)| \leq 1\), \(\omega(0) = 0\), and \(|\omega(z)|<1\) for \(|z| <1\) and such that \(f(z) = \varphi(z)g(\omega(z))\). For the case \(\varphi(z)\equiv z\) the quasi-subordination reduces to the subordination, and for \(\omega(z) \equiv z\) to the majorization. Based on the above definition the authors define the classes \(\mathcal{M}_q(\alpha, \phi)\) and \(\mathcal{L}_q(\alpha, \varphi)\) as the classes of analytic functions \(f\) with \(f(0)=f'(0)-1=0\), and satisfying \[ (1-\alpha)\frac{zf'(z)}{f(z)}+\alpha\left(1+\frac{zf''(z)}{f'(z)}\right)-1\prec_q\varphi(z)-1, \] \[ \left(\frac{zf'(z)}{f(z)}\right)^\alpha\left(1+\frac{zf''(z)}{f'(z)}\right)^{1-\alpha}-1\prec_q\varphi(z)-1, \] respectively. For the above defined class the Fekete-Szegő functional is estimated.
reviewed by: Stanisława Kanas
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 6116340
zbMATH Keywords: quasi-subordination
zbMATH Keywords: alpha-convexity
zbMATH Keywords: alpha logarithmic convexity
zbMATH Keywords: Fekete-Szegő functional
Wikidata QID: Q58695929
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/192956
OpenAlex ID: W2076862700
cites work: Q4149962
cites work: Q4840631
cites work: Quasi-subordination and coefficient conjectures
cites work: Majorizations and quasi-subordinations for certain analytic functions
cites work: Q4063711
cites work: Some inequalities on quasi-subordinate functions
cites work: Q5673687
cites work: Q4150500
cites work: \(\alpha\)-logarithmically convex functions
cites work: A proof of the Bieberbach conjecture
cites work: On the Fekete-Szegő problem for alpha-quasi-convex functions
cites work: Q4339433
cites work: Coefficient bounds for \(p\)-valent functions
cites work: The Fekete-Szegö coefficient functional for transforms of analytic functions
cites work: On the Fekete-Szegö problem for strongly \(\alpha\)-logarithmic quasiconvex functions
cites work: A general approach to the Fekete-Szegö problem
cites work: Q3543179
cites work: Q3634912
cites work: On a class of univalent functions related to complex order
cites work: An unified approach to the Fekete-Szegő problem
cites work: Fekete-Szegő problem for starlike and convex functions of complex order
cites work: Q3985554
cites work: Q4465284
cites work: Q3155743
cites work: Q5312794
cites work: A Coefficient Inequality for Certain Classes of Analytic Functions
cites work: Q5815016
description: scientific article; zbMATH DE number 6116340