International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 329-336
doi:10.1155/S0161171293000390
On certain classes of close-to-convex functions
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.
Abstract
A function f, analytic in the unit disk E and given by , f(z)=z+∑k=2∞anzk is said to be
in the family Kn if and only if Dnf is close-to-convex, where Dnf=z(1−z)n+1∗f, n∈N0={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+1⫅Kn and Kn consists entirely of univalent functions.
Some closure properties of integral operators defined on Kn are given.