Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator

On coefficients of some p-valent starlike functions

“…Applying Theorem 2.6 we easily have the proof of Theorem 2.7. The sharpness of (20) shows the function (16).…”

“…We denote by H the class of functions f (z) which are holomorphic in the open unit disc D = {z ∈ C : |z| < 1}. A function f analytic in a domain D ∈ C is called p-valent in D, if for every complex number w, the equation f (z) = w has at most p roots in D, so that there exists a complex number w 0 such that the equation f (z) = w 0 has exactly p roots in D. The properties of multivalent functions under several operators were established recently in several papers, see for instance [3,6,8,16]. Meromorphic multivalent functions was considered recently in [4,5,9].…”

On certain subclass of p-valent analytic functions associated with differintegral operator

“…Remark 3.1. If we put m = 0, α = λ, β = µ and γ = η, then this result is reduced into the class of functions M λ p (µ, η; γ; φ) which is studied by [24].…”