International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3351-3357
doi:10.1155/IJMMS.2005.3351

A note on a multiplier of the Nörlund means and convex maps of the unit disc

Abstract

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.