International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 495-501
On some classes of analytic functions
Mathematics Department, Science College of Education for Girls, Sitteen Road, Malaz, Riyadh, Saudi Arabia
Received 18 April 1986
Copyright © 1987 Khalida I. Noor and Haila Madifer. 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.
Let , be any numbers and let be the class of functions of analytic in the unit disc for which
where and are analytic in with . Moulis  gave a sufficient condition and a necessary condition on parameters and for the class to consist of univalent functions if and are taken to be convex univalent functions in . In fact he proved that if where and are convex and , , , then is univalent in .
In this paper we consider the class in more general way and show that it contains the class of functions with bounded boundary rotation and many other classes related with it. Some coefficient results, arclength problem, radius of convexity and other problems are proved for certain cases. Our results generalize many previously known ones.