Subclass of analytic functions defined by $ q $-derivative operator associated with Pascal distribution series

B. A. Frasin; M. Darus; B. A. Frasin; M. Darus

doi:10.3934/math.2021295

AIMS Mathematics

2021, Volume 6, Issue 5: 5008-5019. doi: 10.3934/math.2021295

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Subclass of analytic functions defined by $ q $-derivative operator associated with Pascal distribution series

B. A. Frasin ^{1
,
,},
M. Darus ²

1.
Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan
2.
Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia

Received: 19 December 2020 Accepted: 23 February 2021 Published: 04 March 2021
MSC : 30C45, 05A30

The purpose of the present paper is to find the necessary and sufficient condition and inclusion relation for Pascal distribution series to be in the subclass $ \mathcal{TC}_{q}(\lambda, \alpha) $ of analytic functions defined by $ q $-derivative operator. Further, we consider an integral operator related to Pascal distribution series, and several corollaries and consequences of the main results are also considered.
- analytic functions,
- Hadamard product,
- q-starlike functions,
- q-convex functions,
- Pascal distribution series
Citation: B. A. Frasin, M. Darus. Subclass of analytic functions defined by $ q $-derivative operator associated with Pascal distribution series[J]. AIMS Mathematics, 2021, 6(5): 5008-5019. doi: 10.3934/math.2021295

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Abstract

The purpose of the present paper is to find the necessary and sufficient condition and inclusion relation for Pascal distribution series to be in the subclass $ \mathcal{TC}_{q}(\lambda, \alpha) $ of analytic functions defined by $ q $-derivative operator. Further, we consider an integral operator related to Pascal distribution series, and several corollaries and consequences of the main results are also considered.

References

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