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A new subclass of Ma-Minda starlike functions associated with a heart-shaped curve | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 4، دوره 16، شماره 7، مهر 2025، صفحه 37-46 اصل مقاله (975.4 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.29486.4235 | ||
| نویسندگان | ||
| Vahid Vesali؛ Shahram Najafzadeh* | ||
| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| تاریخ دریافت: 03 بهمن 1401، تاریخ بازنگری: 12 اسفند 1402، تاریخ پذیرش: 23 تیر 1403 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Unit disk؛ Analytic functions؛ Starlike function؛ Subordination؛ Radius problems؛ Coefficients problems | ||
| مراجع | ||
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