فهرست نشریات علمی دسترسی آزاد ایران

In this paper, we extend the $q$-derivative operator, which plays an essential role in quantum calculus. Indeed, by using the Hadamard product and generalized Koebe function we define the following $(\alpha,\beta,\gamma)$-derivative operator\begin{equation*}    {\rm d}_{\alpha,\beta,\gamma} f(z)=\frac{1}{z}\left\{f(z)*\mathfrak{L}_{\alpha,\beta,\gamma}(z)\right\},\end{equation*}where\begin{equation*}    \mathfrak{L}_{\alpha,\beta,\gamma}(z)=\frac{2(1-\gamma)z}{(1-\alpha z)(1-\beta z)},\end{equation*}and $\alpha\in[-1,1]$, $\beta\in[-1,1]$, $\alpha\beta\neq \pm1$ and $\gamma\in[0,1)$. Then by subordination relation, the operator ${\rm d}_{\alpha,\beta,\gamma} f(z)$, and a special function $\phi_\delta(z)=1+\delta z/\exp(\delta z)$ ($0<\delta\leq1$), we define a new particular Ma-Minda class. We investigate some properties of this class, such as, radius problem and coefficient estimate.