An application of the distribution series for certain analytic function classes

Abstract

For the generalized distribution with the Pascal model defined by P(X = j) = ( j + t - 1 t - 1 ) pj (1 - p)t j ∈ {0, 1, 2, 3, ...} , let UP(λ, α, μ) and HP(λ, α) represent the analytic function classes in the open unit disk D = {z: z ∈ C and |z| < 1}. The main aim of this paper is to derive the sufficient conditions for functions in these classes.