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Properties of Certain Subclasses of Analytic Functions Involving q-Poisson Distribution

Bilal Khan1,*, Zhi-Guo Liu1, Nazar Khan2, Aftab Hussain3, Nasir Khan4, Muhammad Tahir2

1 School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China
2 Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, 22010, Pakistan
3 Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
4 Department of Mathematics, FATA University, Akhorwal (Darra Adam Khel), FR Kohat, 26000, Pakistan

* Corresponding Author: Bilal Khan. Email: email

(This article belongs to this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 131(3), 1465-1477.


By using the basic (or q)-Calculus many subclasses of analytic and univalent functions have been generalized and studied from different viewpoints and perspectives. In this paper, we aim to define certain new subclasses of an analytic function. We then give necessary and sufficient conditions for each of the defined function classes. We also study necessary and sufficient conditions for a function whose coefficients are probabilities of q-Poisson distribution. To validate our results, some known consequences are also given in the form of Remarks and Corollaries.


Cite This Article

Khan, B., Liu, Z., Khan, N., Hussain, A., Khan, N. et al. (2022). Properties of Certain Subclasses of Analytic Functions Involving q-Poisson Distribution. CMES-Computer Modeling in Engineering & Sciences, 131(3), 1465–1477.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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