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Compositions of harmonic mappings and biharmonic mappings. (English) Zbl 1209.30009
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.
MSC:
30C65Quasiconformal mappings in n and other generalizations
30C45Special classes of univalent and multivalent functions
30C20Conformal mappings of special domains