Abstract
We give coefficient estimates for a class of close-to-convex harmonic mappings , and discuss the Fekete–Szegő problem of it. We also determine a disk
in which the partial sum
is close-to-convex for each
. Then, we introduce two classes of polyharmonic mappings
and
, consider the starlikeness and convexity of them and obtain coefficient estimates for them. Finally, we give a necessary condition for a mapping
to be in the class
.
Acknowledgements
The authors are indebted to the referees for their helpful remarks.
Notes
1 The research was partly supported by Hunan Provincial Innovation Foundation for Postgraduates [number 125000-4242]; CIMO Scholarship of Finland and China Scholarship Council, Academy of Finland [number 269260] and National Natural Science Foundation of China.