Coefficient estimates and the Fekete-Szeg\H o problem for certain classes of polyharmonic mappings

Jiaolong Chen; Antti Rasila; Xiantao Wang

Coefficient estimates and the Fekete-Szeg\H o problem for certain classes of polyharmonic mappings

Complex Variables 2013-10-01 v1

Authors: Jiaolong Chen , Antti Rasila , Xiantao Wang

Abstract

We give coefficient estimates for a class of close-to-convex harmonic mappings, and discuss the Fekete-Szeg\H{o} problem of it. We also introduce two classes of polyharmonic mappings $\mathcal{HS}_{p}$ and $\mathcal{HC}_{p}$ , consider the starlikeness and convexity of them, and obtain coefficient estimates on them. Finally, we give a necessary condition for a mapping $F$ to be in the class $\mathcal{HC}_{p}$ .

Keywords

polyharmonic mappings coefficient estimates fekete-szeg\H{o} problem close-to-convex harmonic mappings starlikeness convexity variational bivectors

Cite

@article{arxiv.1309.7433,
  title  = {Coefficient estimates and the Fekete-Szeg\H o problem for certain classes of polyharmonic mappings},
  author = {Jiaolong Chen and Antti Rasila and Xiantao Wang},
  journal= {arXiv preprint arXiv:1309.7433},
  year   = {2013}
}

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14 pages, 2 figures

Coefficient estimates and the Fekete-Szeg\H o problem for certain classes of polyharmonic mappings

Abstract

Keywords

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