Some properties of analytic functions relating to the Miller and Mocanu result

Let P(α) be the class of analytic functions p(z) in the open unit disc U with p(0) = 1 and | arg p(z)| < π 2 α (z ∈ U) for some real α > 0. The object of the present paper is to discuss some properties of p(z) in the class P(α). Furthermore, an example for our results is shown.