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http://dx.doi.org/10.5666/KMJ.2021.61.1.99

Subclasses of Starlike and Convex Functions Associated with Pascal Distribution Series  

Frasin, Basem Aref (Faculty of Science, Department of Mathematics, Al al-Bayt University)
Swamy, Sondekola Rudra (Department of Computer Science and Engineering, RV College of Engineering)
Wanas, Abbas Kareem (Department of Mathematics, College of Science, University of Al-Qadisiyah)
Publication Information
Kyungpook Mathematical Journal / v.61, no.1, 2021 , pp. 99-110 More about this Journal
Abstract
In the present paper, we determine new characterisations of the subclasses ����∗��(α, β; γ) and ������(α, β; γ) of analytic functions associated with Pascal distribution series ${\Phi}^m_q(z)=z-{\sum_{n=2}^{\infty}}(^{n+m-2}_{m-1})q^{n-1}(1-q)^mz^n$. Further, we give necessary and sufficient conditions for an integral operator related to Pascal distribution series ${\mathcal{G}}^m_qf(z)={\int_{0}^{z}}{\frac{{\Phi}^m_q(t)}{t}}dt$ to belong to the above classes. Several corollaries and consequences of the main results are also considered.
Keywords
Analytic functions; Hadamard product; Pascal distribution series;
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