International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 57, Pages 3599-3607
doi:10.1155/S0161171203301267
On k-nearly uniform convex property in generalized Cesàro sequence spaces
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Received 19 January 2003
Copyright © 2003 Winate Sanhan and Suthep Suantai. 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
We define a generalized Cesàro sequence space ces(p),
where p=(pk) is a bounded sequence of positive real
numbers, and consider it equipped with the Luxemburg norm. The
main purpose of this paper is to show that ces(p) is
k-nearly uniform convex (k-NUC) for k≥2 when limn→∞infpn>1. Moreover, we also obtain
that the Cesàro sequence space cesp(where 1<p<∞) is k-NUC, kR, NUC, and has a drop property.