SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES

Let A be the space of functions analytic in the unit disk D = {z:|z| < 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f(0) = f’(0)-1 = 0 and|f’(z)(z/f(z))~2-1|<1(|z|<1).Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f(0) = f’(0)-1 = 0and|zf’(z)-f(z)|<1/2(|z|<1).In this article,we discuss the properties of U and Ω.