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Pascal distribution series for subclasses of analytic functions associated with conic domains

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Abstract

In the present paper, we determine sufficient conditions for the Pascal distribution series \(P(X=r)=\left( {\begin{array}{c}r+m-1\\ m-1\end{array}}\right) \,q^{r}(1-q)^{m},\) to be in the subclasses of k-parabolic functions and k-uniformly convex functions associated with conic domains. Further, we consider an integral operator related to Pascal distribution series. Some interesting special cases of our main results are also considered.

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Acknowledgements

The authors would like to thank the referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Al al-Bayt University, Al-Mafraq, Jordan

    B. A. Frasin

  2. Department of Mathematical Engineering, Faculty of Arts and Sciences, Istanbul Technical University, Istanbul, Turkey

    S. M. Aydoğan

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  1. B. A. Frasin
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  2. S. M. Aydoğan
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Correspondence to B. A. Frasin.

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Frasin, B.A., Aydoğan, S.M. Pascal distribution series for subclasses of analytic functions associated with conic domains. Afr. Mat. 32, 105–113 (2021). https://doi.org/10.1007/s13370-020-00813-1

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