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.
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
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.
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