Initial coefficient bounds for certain new subclasses of bi-univalent functions with bounded boundary rotation

Abstract

In the current article, we introduced new subclasses of bi-univalent functions associated with bounded boundary rotation. For these new classes, the authors first obtained two initial coefficient bounds. They also verified the special cases where the familiar Brannan and Clunie's conjecture were satisfied. Furthermore, the famous Fekete-Szegö inequality was obtained for the newly defined subclasses of bi-univalent functions, and some of the results improved the earlier results available in the literature.

Keywords

• analytic
• univalent
• close-to-star
• close-to-convex
• bounded boundary rotation
• coefficient estimate