Abstract

A function f, analytic in the unit disk E and given by , f(z)=z+k=2anzk is said to be in the family Kn if and only if Dnf is close-to-convex, where Dnf=z(1z)n+1f, nN0={0,1,2,} and denotes the Hadamard product or convolution. The classes Kn are investigated and some properties are given. It is shown that Kn+1Kn and Kn consists entirely of univalent functions. Some closure properties of integral operators defined on Kn are given.