A subclass 𝒞 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 𝒞 p ( λ , μ ) .