Convex subclass of harmonic starlike functions

Abstract

Complex valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h + (g) over bar, where h and g are analytic in U. We define and investigate a convex subclass of harmonic starlike functions of order alpha (0 less than or equal to a < 1). We obtain coefficient conditions, extreme points, distortion bounds, convolution conditions, and convex combination for the above class of harmonic functions.