A New Subclass of Analytic Functions Related to Mittag-Leffler Type Poisson Distribution Series

The object of this work is to an innovation of a class k − U ~ S T s ℏ , υ , τ , ι , ς in Y with negative coefficients, further determining coefficient estimates, neighborhoods, partial sums, convexity, and compactness of this specified class.

Poisson distribution series on a general class of analytic functions

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

Differential subordination results for holomorphic functions associated with Wanas Operator and Poisson Distribution series

In the current paper, we introduce a new family for holomorphic functions defined by Wanas operator associated with Poisson distribution series. Also we derive some interesting geometric properties for functions belongs to this family.

On certain subclasses of analytic functions associated with Poisson distribution series

In this paper, we find the necessary and sufficient conditions, inclusion relations for Poisson distribution series $\mathcal{K}\left( {{\rm{m, z}}} \right) = {\rm{z + }}\sum\limits_{{\rm{n}} = 2}^\infty {{{{{\rm{m}}^{{\rm{n}} - 1}}} \over {\left( {n - 1} \right)!}}{{\rm{e}}^{ - {\rm{m}}}}{{\rm{z}}^{\rm{n}}}} $ to be in the subclasses 𝒮(k, λ) and 𝒞(k, λ) of analytic functions with negative coefficients. Further, we obtain necessary and sufficient conditions for the integral operator ${\rm{\mathcal{G}}}\left( {{\rm{m}},{\rm{z}}} \right) = \int_0^{\rm{z}} {{{{\rm{\mathcal{F}}}\left( {{\rm{m}},{\rm{t}}} \right)} \over {\rm{t}}}} {\rm{dt}}$ to be in the above classes.