A constructive method for starlike harmonic mappings
type: Item
instance of: scholarly article
title: A constructive method for starlike harmonic mappings
zbMATH Open document ID: 0676.30014
DOI: 10.1007/BF01396972
author: S. H. Smith
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133311
review text: The authors expand an idea of the reviewer according to which certain conformal mappings f render a functional \(\nu\) (f) minimum within the class of all (suitably normalized) holomorphic functions. The authors extend this principle to functions f which satisfy a differential equation of Beltrami-type \(\bar f_{\bar z}(z)=a(z)f_ z(z)\). The advantage of this principle is its easy transition to numerical computations. The authors describe this method and present some examples \((a(z)=\rho z\) \((0<\rho <1)\), \(\nu (z)=Im z)\) for which they know the exact results. In the case of the chosen \(\nu\) the numerical procedure is reduced to linear programming. The numerical figures shown are at least partially quite accurate.
Mathematics Subject Classification ID: 30C75
Mathematics Subject Classification ID: 30C30
zbMATH DE Number: 4107160
zbMATH Keywords: extremal principles for harmonic functions
reviewed by: Gerhard Opfer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4107160