New Approach for Certain Analytic Functions

Let A be the class of functions f(z) in the open unit disc U with f(۰)=۰. For this class A, we introduce the subclass A_{n}(\alpha) of A consisting of f(z)=\alpha z+\sum\limits_{k=۱}^{\infty} a_{۱+\frac{k}{n}} z^{۱+\frac{k}{n}}, \quad (n \in \mathbb{N}), for \alpha>۰.For functions f(z) \in A_{n}(\alpha), we discuss some coefficient problems, subordination problems and argument problems with some examples of the results.

کلیدواژه ها:

Analytic function ، Coefficient inequality ، Subordination ، Argument problem