Initial Coefficient Bounds for Certain New Subclasses of Bi-Univalent Functions Involving Mittag–Leffler Function with Bounded Boundary Rotation

Abstract

By using the Mittag–Leffler function associated with functions of bounded boundary rotation, the authors introduce a few new subclasses of bi-univalent functions involving the Mittag–Leffler function with bounded boundary rotation in the open unit disk D. For these new classes, the authors establish initial coefficient bounds of |a2| and |a3|. Furthermore, the famous Fekete–Szegö coefficient inequality is also obtained for these new classes of functions.

Keywords

• holomorphic
• bi-univalent functions
• convolution
• Mittag–Leffler function
• bounded boundary rotation