Certain Univalent Harmonic Functions

A function f(z) = u(z) + iv(z) is harmonic in △ ={ z : |z| < 1} if u(z) and v(z) are real harmonic in A. We can also write f(z) = h(z) + g(z), where h(z) and g(z) are analytic in A. Letwhere a1 = 1, |b1|< 1. The family of harmonic functions in A will be denoted by H.In this paper we consider the subclasses of Hand their linear combination Rh(α, λ) =where 0≤a < 1, λ > 0.A sufficient and necessary condition that the function / belongs to one of these classes is shown. From these new definitions we obtain some coefficient inequalities and the estimates of module and argument. Let H denotes the subclass of H consisting of functions that h(z) - z has negative and g(z) has positive coefficients. Furthermore, several inclusion relations, distortion theorem, extreme points and convolution condition for these classes PH(α), NH(α) and RH(α, λ) are obtained.