On a subclass of close-to-convex harmonic mappings

Abstract

We introduce a new subclass of close-to-convex harmonic mappings in the unit disk, which originates from the work of P. Mocanu on univalent mappings. We also give coefficient estimates, and discuss the Fekete-Szegő problem, for this class of mappings. Furthermore, we consider growth, covering and area theorems of the class. In addition, we determine a disk in which the partial sum is close-to-convex for each function of the class . Finally, for certain values of the parameters and , we solve the radii problems related to starlikeness and convexity of functions of this class.

Keywords:

• Harmonic mapping
• coefficient estimate
• Fekete–Szegő problem
• growth theorem
• covering theorem
• area theorem
• partial sum
• close-to-convex function
• starlike function
• convex function

AMS Subject Classifications:

• 0C45
• 30C50
• 58E20
• 30C80

Acknowledgements

The authors are indebted to the anonymous referees for their very careful reading of the manuscript and for their valuable suggestions that helped to improve the quality of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the Natural Science Foundation of China under [grant number 11371126]; the Foundation of Educational Committee of Hunan Province under [grant number 15C1089]. The third author was supported by Academy of Finland [grant number 289576].