Some Properties for Subordinations of Analytic Functions

Abstract

Let the class of functions of f(z) of the form f(z)=z+∑k=2∞akzk, 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)∈A provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of f(z)∈A with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results.

Keywords

• analytic function
• starlike function of order α
• convex function of order α
• subordination
• differential subordinaton