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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 476363, 9 pages
http://dx.doi.org/10.1155/2013/476363
Research Article

On the Domain of the Triangle on the Spaces of Null, Convergent, and Bounded Sequences

1Department of Mathematics and Computer Sciences, Avenue “Mother Teresa” Nr=5, 10000 Prishtinë, Kosovo
2Department of Mathematics, Faculty of Arts and Sciences, Fatih University, The Hadimköy Campus, Büyükçekmece, 34500 İstanbul, Turkey

Received 17 January 2013; Accepted 7 May 2013

Academic Editor: Douglas Anderson

Copyright © 2013 Naim L. Braha and Feyzi Başar. 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 introduce the spaces of -null, -convergent, and -bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute -, -, and -duals of these spaces. Finally, we characterize some classes of matrix transformations from the spaces of -bounded and -convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.