Abstract and Applied Analysis
Volume 2011 (2011), Article ID 213878, 14 pages
http://dx.doi.org/10.1155/2011/213878
Research Article

Some Topological and Geometrical Properties of a New Difference Sequence Space

Serkan Demiriz1 and Celal Çakan2

1Department of Mathematics, Faculty of Arts and Science, Gaziosmanpaşa University, 60250 Tokat, Turkey
2Faculty of Education, Inönü University, 44280 Malatya, Turkey

Received 9 August 2010; Accepted 25 January 2011

Academic Editor: Narcisa C. Apreutesei

Copyright © 2011 Serkan Demiriz and Celal Çakan. 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 new difference sequence space 𝑎 𝑟 𝑝 ( Δ ) . Further, it is proved that the space 𝑎 𝑟 𝑝 ( Δ ) is the BK-space including the space 𝑏 𝑣 𝑝 , which is the space of sequences of pbounded variation. We also show that the spaces 𝑎 𝑟 𝑝 ( Δ ) , and ℓ 𝑝 are linearly isomorphic for 1 ≤ 𝑝 < ∞ . Furthermore, the basis and the 𝛼 - , 𝛽 - and 𝛾 - duals of the space 𝑎 𝑟 𝑝 ( Δ ) are determined. We devote the final section of the paper to examine some geometric properties of the space 𝑎 𝑟 𝑝 ( Δ ) .