Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 426357, 17 pages
http://dx.doi.org/10.1155/2012/426357
Research Article

On Some Lacunary Almost Convergent Double Sequence Spaces and Banach Limits

Department of Mathematics, Sakarya University, 54187 Sakarya, Turkey

Received 13 June 2012; Accepted 9 July 2012

Academic Editor: Chaitan Gupta

Copyright © 2012 Metin Başarır and Şükran Konca. 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. 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
  2. F. Moricz 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
  3. 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
  4. M. Başarır and O. Sonalcan, “On some double sequence spaces,” Indian Academy of Mathematics. Journal, vol. 21, no. 2, pp. 193–200, 1999. View at Google Scholar · View at Zentralblatt MATH
  5. M. 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
  6. M. 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
  7. 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
  8. M. Mursaleen and E. Savaş, “Almost regular matrices for double sequences,” Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences, vol. 40, no. 1-2, pp. 205–212, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. E. Savaş and R. F. Patterson, “On some double almost lacunary sequence spaces defined by Orlicz functions,” Filomat, Faculty of Sciences and Mathematics. University of Niš, no. 19, pp. 35–44, 2005. View at Google Scholar · View at Zentralblatt MATH
  10. E. Savaş and R. F. Patterson, “Double sequence spaces characterized by lacunary sequences,” Applied Mathematics Letters, vol. 20, no. 9, pp. 964–970, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. A. Gokhan, M. Et, and M. Mursaleen, “Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 548–555, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. M. Mursaleen and S. A. Mohiuddine, “On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 142–149, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. 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
  14. G. A. Anastassiou, M. Mursaleen, and S. A. Mohiuddine, “Some approximation theorems for functions of two variables through almost convergence of double sequences,” Journal of Computational Analysis and Applications, vol. 13, no. 1, pp. 37–46, 2011. View at Google Scholar · View at Zentralblatt MATH
  15. I. J. Maddox, “A new type of convergence,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 83, no. 1, pp. 61–64, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. I. J. Maddox, “On strong almost convergence,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 85, no. 2, pp. 345–350, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. Başarır, “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
  18. G. Das and S. K. Mishra, “Banach limits and lacunary strong almost convergence,” Journal of Orissa Mathematical Society, vol. 2, no. 2, pp. 61–70, 1983. View at Google Scholar · View at Zentralblatt MATH
  19. M. Başarır, “On some new sequence spaces,” Rivista di Matematica della Università di Parma, vol. 5, no. 1, pp. 339–347, 1992. View at Google Scholar · View at Zentralblatt MATH
  20. G. Das and S. K. Sahoo, “On some sequence spaces,” Journal of Mathematical Analysis and Applications, vol. 164, no. 2, pp. 381–398, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH