International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3351-3357
A note on a multiplier of the Norlund means and convex maps of the unit disc
American College of Switzerland, Leysin 1854, Switzerland
Received 27 January 2005; Revised 3 June 2005
Copyright © 2005 Ziad S. Ali. 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.
Important and interesting results which are already known such as those by Pólya and Schoenberg in (1958), Başgöze et al. in (1970), and Ali in (1973), and which are related to convex maps of the unit disc are presented in this note by a more general, unified, and different method. The method considers the product of a nontrivial multiplier with the Norlund means, and shows how the known results indicated above are reproduced again as special cases.