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 ɛ A satisfying the conditions f(0)=f′(0)−1=0 and |f′(z)(zf(z))2-1|<1(|z|<1). Also, let Ω denote the set of all functions f ɛ A satisfying the conditions f(0) = f′(0)-1 = 0 and |zf′(z)-f(z)|<12(|z|<1). In this article, we discuss the properties of U and Ω.