Landau–Bloch type theorems for certain biharmonic mappings

Abstract

In this paper, two versions of Landau–Bloch type theorems for biharmonic mappings are provided by applying the geometric method and establishing better coefficient estimates for bounded and normalized planar harmonic mappings. In particular, we pose a conjecture for the sharp version of Landau–Bloch type theorem for certain bounded harmonic mappings. The results in the presented paper improve a related result of the earlier author.

COMMUNICATED BY:

• X. Huang

Keywords:

• Bloch constant
• biharmonic mapping
• harmonic mapping
• univalent

AMS Subject Classifications:

• 30C99
• 30C62

Acknowledgements

The authors of this paper thank the referees very much for their valuable comments and suggestions to this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ming-Sheng Liu http://orcid.org/0000-0002-2644-6997

Additional information

Funding

This research is supported by the Guangdong Natural Science Foundation [grant number 2018A030313508].