Coefficient inequality for a subclass of biholomorphic mappings in several complex variables

Abstract

Let be the familiar class of starlike functions of order in the unit disk. In Keogh and Merkes proved that for a function in the class , then

In this paper, we investigate the corresponding problem for the subclass of starlike mappings of order defined on the unit ball in a complex Banach space, on the unit polydisk in and the bounded starlike circular domain in , respectively.

Keywords:

• Starlike mappings of order of
• sharp coefficient bound
• Fekete-Szegö problem

AMS Subject Classifications:

• Primary: 32H02
• Secondary: 30C45

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NNSF of China [grant number 11561030], [grant number 11261022]; the Jiangxi Provincial Natural Science Foundation of China [grant number 20152ACB20002]; [grant number 20161BAB201019]; Natural Science Foundation of Department of Education of Jiangxi Province, China [grant number GJJ150301].