Abstract and Applied Analysis
Volume 2011 (2011), Article ID 950364, 9 pages
http://dx.doi.org/10.1155/2011/950364
Research Article

The Cesáro Core of Double Sequences

Kuddusi Kayaduman1 and Celal Çakan2

1Department of Mathematics, Faculty of Science and Arts, Gaziantep University, 27310 Gaziantep, Turkey
2Faculty of Education, Inönü University, 44280 Malatya, Turkey

Received 24 March 2011; Accepted 24 May 2011

Academic Editor: Malisa R. Zizovic

Copyright © 2011 Kuddusi Kayaduman 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 have characterized a new type of core for double sequences, 𝑃 𝐶 -core, and determined the necessary and sufficient conditions on a four-dimensional matrix 𝐴 to yield 𝑃 𝐶 -core { 𝐴 𝑥 } ⊆ 𝛼 ( 𝑃 -core { 𝑥 } ) for all ℓ ∞ 2 .