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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 949282, 10 pages
http://dx.doi.org/10.1155/2013/949282
Research Article

Domain of the Double Sequential Band Matrix in the Sequence Space

Department of Mathematics, Faculty of Arts and Sciences, Fatih University, The Hadımköy Campus, Büyükçekmece, 34500 Istanbul, Turkey

Received 17 October 2012; Accepted 29 January 2013

Academic Editor: Ferhan M. Atici

Copyright © 2013 Havva Nergiz 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

The sequence space was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix in the sequence space has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space of nonabsolute type has been studied which is the domain of the generalized difference matrix in the sequence space . Furthermore, the alpha-, beta-, and gamma-duals of the space have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space to the spaces , c and c0 have been characterized. Additionally, the characterizations of some other matrix transformations from the space to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.