Bulletin of the Belgian Mathematical Society - Simon Stevin

Compositions of harmonic mappings and biharmonic mappings

Shaolin Chen, Saminathan Ponnusamy, and Xiantao Wang

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Abstract

The aim of this paper is twofold. First, we investigate the properties of the composition of harmonic mappings with harmonic mappings, and the composition of biharmonic mappings with harmonic mappings. Second, we consider the Goodman-Saff conjecture for biharmonic mappings in the unit disk. In fact, we show that the answer to the Goodman-Saff conjecture is positive for a special class of univalently biharmonic mappings which contains the set of all harmonic univalent mappings.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 4 (2010), 693-704.

Dates
First available in Project Euclid: 24 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1290608195

Digital Object Identifier
doi:10.36045/bbms/1290608195

Mathematical Reviews number (MathSciNet)
MR2778445

Zentralblatt MATH identifier
1209.30009

Subjects
Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C20: Conformal mappings of special domains

Keywords
Analytic functions univalent harmonic mappings biharmonic mappings and convex functions

Citation

Chen, Shaolin; Ponnusamy, Saminathan; Wang, Xiantao. Compositions of harmonic mappings and biharmonic mappings. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 4, 693--704. doi:10.36045/bbms/1290608195. https://projecteuclid.org/euclid.bbms/1290608195


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