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Abstract and Applied Analysis
Volume 2014, Article ID 858704, 9 pages
http://dx.doi.org/10.1155/2014/858704
Research Article

On the Paranormed Nörlund Sequence Space of Nonabsolute Type

1Department of Mathematics, Uşak University, 1 Eylül Campus, 64200 Uşak, Turkey
2Department of Mathematics, Fatih University, Hadımköy Campus, Büyükçekmece, 34500 İstanbul, Turkey

Received 3 December 2013; Accepted 2 February 2014; Published 26 March 2014

Academic Editor: M. Mursaleen

Copyright © 2014 Medine Yeşilkayagil 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

Maddox defined the space of the sequences such that , in Maddox, 1967. In the present paper, the Nörlund sequence space of nonabsolute type is introduced and proved that the spaces and are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the space are computed and the basis of the space is constructed. The classes and of infinite matrices are characterized. Finally, some geometric properties of the space are investigated.