Radius constants for functions with the prescribed coefficient bounds
type: Item
instance of: scholarly article
title: Radius constants for functions with the prescribed coefficient bounds
zbMATH Open document ID: 1470.30004
DOI: 10.1155/2014/454152
author: Sumit Nagpal
author: Om P. Ahuja
author: V. Ravichandran
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: For an analytic univalent function \(f(z) = z + \sum_{n = 2}^{\infty} a_n z^n\) in the unit disk, it is well-known that \(\left|a_n\right| \leq n\) for \(n \geq 2\). But the inequality \(\left|a_n\right| \leq n\) does not imply the univalence of \(f\). This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of order \(\alpha\) (\(0 \leq \alpha < 1\)) for functions with prescribed coefficient bound on the analytic part.
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C50
zbMATH DE Number: 7022405
Wikidata QID: Q59038319
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/454152
OpenAlex ID: W2162173617
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description: scientific article; zbMATH DE number 7022405