Third Hankel determinant for alpha-starlike functions

Abstract

In this paper we investigate the third Hankel determinant, H₃(1), for normalized univalent functions f(z) = z + a₂ z² + ... belonging to the class of α-starlike functions denoted by M_α. This class includes two important subclasses of the family of univalent functions - starlike and convex functions denoted by S^∗ and C. Our results therefore includes the special cases of the third Hankel determinants for the two classes of functions.