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Chen, J.; Rasila, A.; Wang, X.

Coefficient estimates and radii problems for certain classes of polyharmonic mappings. (English) Zbl 1312.31003

Complex Var. Elliptic Equ. 60, No. 3, 354-371 (2015).
Summary: We give coefficient estimates for a class of close-to-convex harmonic mappings \(\mathcal F\), and discuss the Fekete-Szegő problem of it. We also determine a disk \(| z|<r\) in which the partial sum \(s_{m,n}(f)\) is close-to-convex for each \(f\in\mathcal F\). Then, we introduce two classes of polyharmonic mappings \(\mathcal{HS}_p\) and \(\mathcal{HC}_p\), consider the starlikeness and convexity of them and obtain coefficient estimates for them. Finally, we give a necessary condition for a mapping \(F\) to be in the class \(\mathcal{HC}_p\).

Cited in 8 Documents

MSC:

31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable

Keywords:

harmonic mappings; polyharmonic mappings; coefficient estimates; Fekete-Szegő problem; starlike functions; convex functions
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