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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 465364, 9 pages
http://dx.doi.org/10.1155/2012/465364
Research Article

Invariant and Absolute Invariant Means of Double Sequences

1Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Received 20 February 2012; Revised 17 April 2012; Accepted 28 April 2012

Academic Editor: Sivaram K. Narayan

Copyright © 2012 Abdullah Alotaibi et al. 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 examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.