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The object of the present paper is to derive certain sufficient conditions for univalence, p-valently starlikeness and p-valently close-to-convexity of analytic functions in the unit disk. Our results extend and improve some results due to Owa , Frasin and Darus  and Chen .
A subclass Ꮿ p (λ, µ) (p ∈ N, 0 < λ < 1, −λ µ < 1) of p-valently convex functions in the open unit disk U is introduced. The object of the present paper is to discuss some interesting properties of functions belonging to the class Ꮿ p (λ, µ).
By using the method of differential subordination, we obtain some sufficient conditions for strongly p-valent starlikeness.