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The purpose of the present paper is to determine the necessary and sufficient conditions for the power series Bμ whose coefficients are probabilities of the Borel distribution to be in the family H(λ, σ, δ, μ) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.
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Wanas et al. (2020) studied this question.
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