International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 329-336

On certain classes of close-to-convex functions

Khalida Inayat Noor

Mathematics Department, College of Science, P.O. Box 2455, King Saud University, Riyadh 11451, Saudi Arabia

Received 30 May 1991; Revised 27 September 1991

Copyright © 1993 Khalida Inayat Noor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.