Properties of harmonic functions which are convex of order β with respect to conjugate points - Aini Janteng; Suzeini Abdul Halim (Hikari Ltd, 2013)
Let H denote the class of functions f which are harmonic and univalent in the open unit disc D = {z : |z| < 1}. This paper defines and investigates a family of complex-valued harmonic functions that are orientation preserving and univalent in D and are related to the functions convex of order β (0 ≤ β < 1), with respect to conjugate points. We obtain coefficient conditions, growth result, extreme points, convolution and convex combinations for the above harmonic functions.