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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 57, Pages 3599-3607
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 k2 when limninfpn>1. Moreover, we also obtain that the Cesàro sequence space cesp(where1<p<) is k-NUC, kR, NUC, and has a drop property.