Convolution and subordination in the convex hull of convex mappings

Abstract In this work we give an extension of the Ruscheweyh and Stankiewicz theorem [S. Ruscheweyh, J. Stankiewicz, Subordination under convex univalent functions, Bull. Polish Acad. Sci. Math. 33 (1985) 499–502] on the subordination under convex functions in the unit disc Δ = { z : | z | 1 } . We prove that if f ≺ F ∈ c o ¯ K and g ≺ G ∈ c o ¯ K , then f ⋆ g ≺ F ⋆ G where ≺ denotes the subordination, ⋆ denotes the Hadamard product and c o ¯ K is the closed convex hull of the class of convex functions.