Some classes of order \alpha\ for second-order differential inequalities

For analytic functions f(z) in the open unit disk U with f(0)=f’(0)-1=0, S. S. Miller and P. T. Mocanu (Integral Transform. Spec. Funct. 19(2008)) have considered some sufficient problems for starlikeness. The object of the present paper is to discuss some sufficient problems for f(z) to be in some classes of order \alpha.