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Abstract and Applied Analysis
Volume 2014, Article ID 412974, 6 pages
http://dx.doi.org/10.1155/2014/412974
Research Article

Almost Conservative Four-Dimensional Matrices through de la Vallée-Poussin Mean

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 1 November 2013; Accepted 17 December 2013; Published 2 January 2014

Academic Editor: Mohammad Mursaleen

Copyright © 2014 S. A. Mohiuddine and Abdullah Alotaibi. 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.

Linked References

  1. S. Banach, Théorie des Operations Lineaires, 1932.
  2. G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167–190, 1948. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. A. Mohiuddine, “An application of almost convergence in approximation theorems,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1856–1860, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. Móricz and B. E. Rhoades, “Almost convergence of double sequences and strong regularity of summability matrices,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104, no. 2, pp. 283–294, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Mursaleen and S. A. Mohiuddine, “Banach limit and some new spaces of double sequences,” Turkish Journal of Mathematics, vol. 36, no. 1, pp. 121–130, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Başarir, “On the strong almost convergence of double sequences,” Periodica Mathematica Hungarica, vol. 30, no. 3, pp. 177–181, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. F. Başar and M. Kirişçi, “Almost convergence and generalized difference matrix,” Computers & Mathematics with Applications, vol. 61, no. 3, pp. 602–611, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Čunjalo, “Almost convergence of double subsequences,” Filomat, vol. 22, no. 2, pp. 87–93, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. K. Kayaduman and C. Çakan, “The cesáro core of double sequences,” Abstract and Applied Analysis, vol. 2011, Article ID 950364, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Mursaleen, “Almost strongly regular matrices and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 523–531, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Mursaleen and O. H. H. Edely, “Almost convergence and a core theorem for double sequences,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 532–540, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Zeltser, M. Mursaleen, and S. A. Mohiuddine, “On almost conservative matrix methods for double sequence spaces,” Publicationes Mathematicae Debrecen, vol. 75, no. 3-4, pp. 387–399, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. A. Pringsheim, “Zur theorie der zweifach unendlichen zahlenfolgen,” Mathematische Annalen, vol. 53, no. 3, pp. 289–321, 1900. View at Publisher · View at Google Scholar · View at MathSciNet
  14. B. Altay and F. Başar, “Some new spaces of double sequences,” Journal of Mathematical Analysis and Applications, vol. 309, no. 1, pp. 70–90, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. J. Hamilton, “Transformations of multiple sequences,” Duke Mathematical Journal, vol. 2, no. 1, pp. 29–60, 1936. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. A. Mohiuddine and A. Alotaibi, “Some spaces of double sequences obtained through invariant mean and related concepts,” Abstract and Applied Analysis, vol. 2013, Article ID 507950, 11 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Mursaleen and S. A. Mohiuddine, “Double σ-multiplicative matrices,” Journal of Mathematical Analysis and Applications, vol. 327, no. 2, pp. 991–996, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. M. Mursaleen and S. A. Mohiuddine, “On σ-conservative and boundedly σ-conservative four-dimensional matrices,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 880–885, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  19. P. Schaefer, “Infinite matrices and invariant means,” Proceedings of the American Mathematical Society, vol. 36, pp. 104–110, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. G. M. Robison, “Divergent double sequences and series,” Transactions of the American Mathematical Society, vol. 28, no. 1, pp. 50–73, 1926. View at Publisher · View at Google Scholar · View at MathSciNet
  21. J. P. King, “Almost summable sequences,” Proceedings of the American Mathematical Society, vol. 17, pp. 1219–1225, 1966. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. P. Schaefer, “Matrix transformations of almost convergent sequences,” Mathematische Zeitschrift, vol. 112, pp. 321–325, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. F. Başar and I. Solak, “Almost-coercive matrix transformations,” Rendiconti di Matematica e delle sue Applicazioni, vol. 11, no. 2, pp. 249–256, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. F. Móricz, “Extensions of the spaces c and c0 from single to double sequences,” Acta Mathematica Hungarica, vol. 57, no. 1-2, pp. 129–136, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. Mursaleen and S. A. Mohiuddine, “Regularly σ-conservative and σ-coercive four dimensional matrices,” Computers & Mathematics with Applications, vol. 56, no. 6, pp. 1580–1586, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  26. C. Eizen and G. Laush, “Infinite matrices and almost convergence,” Mathematica Japonica, vol. 14, pp. 137–143, 1969. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet