Let \(\mathcal {A}\) denote the family of analytic functions in the open unit disk \(\mathbb {U}=\{\zeta \in \mathbb {C}:|\zeta |<1\}\). These functions f are normalized under the conditions \(f(0) = 0\) and \(f^{\prime }(0)=1\) in \(\mathbb {U}\) and are given by,
$$\begin{aligned} f(\zeta )=\zeta +\sum _{n=2}^{\infty } o_{n}\zeta ^{n} \end{aligned}$$
(1)
and let \(\mathcal {S}\) be the subclass of \(\mathcal {A}\) consisting of the univalent functions.
Porwal and Dixit14 defined the Mittag-Leffler type Poisson distribution as,
$$\begin{aligned} \mathbb…
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