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Zbl 1209.30009
Chen, Shaolin; Ponnusamy, Saminathan; Wang, Xiantao
Compositions of harmonic mappings and biharmonic mappings. (English)
[J] Bull. Belg. Math. Soc. - Simon Stevin 17, No. 4, 693-704 (2010). ISSN 1370-1444

The authors investigate the properties of the composition of harmonic mappings with harmonic mappings and the composition of biharmonic mappings with harmonic mappings. They give some applications in other areas of biharmonic functions. The proofs for the theorems are rigorous and fair. They give an answer for the Goodman-Saff conjecture for a special class of univalently biharmonic mappings which contains the set of all harmonic univalent mappings.
[Daniel Breaz (Alba Iulia)]

MSC 2000:: *30C65 Quasiconformal mappings in R$\sp n$ and other generalizations
30C45 Special classes of univalent and multivalent functions
30C20 Conformal mappings of special domains

Keywords: univalent function, harmonic mapping; biharmonic mapping; convex function

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