Some Properties for Subordinations of Analytic Functions.

Let the class of functions of f (z) of the form f (z) = z + n-expressionry sumexpressiontion (infinity)(k=2) a(k)z(k), which are denoted by A and called analytic functions in the open-unit disk. There are many interesting properties of the functions f (z) in the class A concerning the subordinations. Applying the three lemmas for f (z) is an element of A provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of f (z) is an element of A with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results.