`Journal of Function Spaces and ApplicationsVolume 2012 (2012), Article ID 465364, 9 pageshttp://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

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.

1. F. Móricz, â€śExtensions of the spaces c and co from single to double sequences,â€ť Acta Mathematica Hungarica, vol. 57, no. 1-2, pp. 129â€“136, 1991.
2. A. Pringsheim, â€śZur Theorie der zweifach unendlichen Zahlenfolgen,â€ť Mathematische Annalen, vol. 53, no. 3, pp. 289â€“321, 1900.
3. H. J. Hamilton, â€śTransformations of multiple sequences,â€ť Duke Mathematical Journal, vol. 2, no. 1, pp. 29â€“60, 1936.
4. M. Mursaleen and S. A. Mohiuddine, â€śAlmost bounded variation of double sequences and some four dimensional summability matrices,â€ť Publicationes Mathematicae Debrecen, vol. 75, no. 3-4, pp. 495â€“508, 2009.
5. G. M. Robison, â€śDivergent double sequences and series,â€ť Transactions of the American Mathematical Society, vol. 28, no. 1, pp. 50â€“73, 1926.
6. M. Mursaleen, â€śOn 𝒜-invariant mean and 𝒜-almost convergence,â€ť Analysis Mathematica, vol. 37, no. 3, pp. 173â€“180, 2011.
7. P. Schaefer, â€śInfinite matrices and invariant means,â€ť Proceedings of the American Mathematical Society, vol. 36, pp. 104â€“110, 1972.
8. M. Mursaleen, â€śOn some new invariant matrix methods of summability,â€ť The Quarterly Journal of Mathematics, vol. 34, no. 133, pp. 77â€“86, 1983.
9. M. Mursaleen and S. A. Mohiuddine, â€śSome inequalities on sublinear functionals related to the invariant mean for double sequences,â€ť Mathematical Inequalities & Applications, vol. 13, no. 1, pp. 157â€“163, 2010.
10. M. Mursaleen and S. A. Mohiuddine, â€śBanach limit and some new spaces of double sequences,â€ť Turkish Journal of Mathematics, vol. 36, pp. 121â€“130, 2012.
11. C. Çakan, B. Altay, and M. Mursaleen, â€śThe σ-convergence and σ-core of double sequences,â€ť Applied Mathematics Letters, vol. 19, no. 10, pp. 1122â€“1128, 2006.
12. C. Çakan, B. Altay, and H. Coşkun, â€śσ-regular matrices and a σ-core theorem for double sequences,â€ť Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 1, pp. 51â€“58, 2009.
13. M. Mursaleen and S. A. Mohiuddine, â€śDouble σ-multiplicative matrices,â€ť Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 991â€“996, 2007.
14. M. Mursaleen and S. A. Mohiuddine, â€śRegularly σ-conservative and σ-coercive four dimensional matrices,â€ť Computers & Mathematics with Applications, vol. 56, no. 6, pp. 1580â€“1586, 2008.
15. M. Mursaleen and S. A. Mohiuddine, â€śOn σ-conservative and boundedly σ-conservative four-dimensional matrices,â€ť Computers & Mathematics with Applications, vol. 59, no. 2, pp. 880â€“885, 2010.
16. M. Mursaleen and S. A. Mohiuddine, â€śInvariant mean and some core theorems for double sequences,â€ť Taiwanese Journal of Mathematics, vol. 14, no. 1, pp. 21â€“33, 2010.
17. F. Móricz and B. E. Rhoades, â€śAlmost convergence of double sequences and strong regularity of summability matrices,â€ť Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104, no. 2, pp. 283â€“294, 1988.
18. G. G. Lorentz, â€śA contribution to the theory of divergent sequences,â€ť Acta Mathematica, vol. 80, pp. 167â€“190, 1948.
19. M. Mursaleen, â€śMatrix transformations between some new sequence spaces,â€ť Houston Journal of Mathematics, vol. 9, no. 4, pp. 505â€“509, 1983.
20. G. Das and S. K. Sahoo, â€śA generalisation of strong and absolute almost convergence,â€ť The Journal of the Indian Mathematical Society, vol. 58, no. 1–4, pp. 65â€“74, 1992.
21. G. Das and B. K. Ray, â€śAbsolute almost convergence and application,â€ť in Modern Methods of Analysis and Its Applications, M. Mursaleen, Ed., pp. 11â€“20, Anamaya, New Delhi, India, 2010.
22. M. Mursaleen and S. A. Mohiuddine, â€śSome new double sequence spaces of invariant means,â€ť Glasnik Matematički, Serija III, vol. 45, no. 65, pp. 139â€“153, 2010.
23. G. Das and B. Kuttner, â€śSpace of absolute almost convergence,â€ť Indian Journal of Mathematics, vol. 28, no. 3, pp. 241â€“257, 1986.