On neighborhoods of analytic functions defined by using Hadamard product

Halit Orhan

We introduce the classes $S_n(\gamma,\beta,\alpha)$ and $\Re_n(\gamma,\beta,\alpha,\mu)$ of functions defined by $f*S_\alpha(z)$ of $f(z)$ and $S_\alpha(z)=\frac 1{(1-z)^2(1-\alpha)}$. By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relations associated with the $(n,\delta)$-neighborhoods of certain subclasses of analytic functions of complex order, which are introduced by means of the Hadamard product.