A new subclass of complex harmonic 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. In this paper, we introduce a class HP(alpha), (alpha greater than or equal to 0) of functions which are harmonic in U. We give sufficient coefficient conditions for normalized harmonic functions in HP(alpha). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.