About this Journal Submit a Manuscript Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 378575, 11 pages
http://dx.doi.org/10.5402/2012/378575
Research Article

Some Almost Lacunary Double Sequence Spaces Defined by Orlicz Functions in 2-Normed Spaces

Ishik University, Erbil, Iraq

Received 16 November 2011; Accepted 25 December 2011

Academic Editor: O. Miyagaki

Copyright © 2012 Orhan Tuğ. 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. 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
  3. 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
  4. A. R. Freedman, J. J. Sember, and M. Raphael, “Some Cesàro-type summability spaces,” Proceedings of the London Mathematical Society. Third Series, vol. 37, no. 3, pp. 508–520, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. A. Fridy and C. Orhan, “Lacunary statistical convergence,” Pacific Journal of Mathematics, vol. 160, no. 1, pp. 43–51, 1993. View at Zentralblatt MATH
  6. J. Li, “Lacunary statistical convergence and inclusion properties between lacunary methods,” International Journal of Mathematics and Mathematical Sciences, vol. 23, no. 3, pp. 175–180, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. R. F. Patterson and E. Savaş, “Lacunary statistical convergence of double sequences,” Mathematical Communications, vol. 10, no. 1, pp. 55–61, 2005. View at Zentralblatt MATH
  8. M. A. Krasnoselskii and Y. B. Rutisky, Convex Function and Orlicz Spaces, Groningen, The Netherlands, Noordhoff, 1961.
  9. W. H. Ruckle, “FK-spaces in which the sequence of coordinate vectors is bounded,” Canadian Journal of Mathematics, vol. 25, pp. 973–978, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. I. J. Maddox, “Sequence spaces defined by a modulus,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 100, no. 1, pp. 161–166, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. B. Tripathy and B. C. Tripathy, “On I-convergent double sequences,” Soochow Journal of Mathematics, vol. 31, no. 4, pp. 549–560, 2005.
  12. S. Gähler, “2-metrische Räume und ihre topologische Struktur,” Mathematische Nachrichten, vol. 26, pp. 115–148, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. Gahler, “Lineare 2-normietre Raume,” Mathematische Nachrichten, vol. 28, pp. 335–347, 1964.
  14. S. Gahler, “Unterschungen uber verallgemeinerte m-metrische Raume.II,” Mathematische Nachrichten, vol. 40, pp. 229–264, 1969.
  15. 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
  16. 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
  17. G. Das and B. K. Patel, “Lacunary distribution of sequences,” Indian Journal of Pure and Applied Mathematics, vol. 20, no. 1, pp. 64–74, 1989. View at Zentralblatt MATH
  18. E. Savaş and R. F. Patterson, “On some double almost lacunary sequence spaces defined by Orlicz functions,” Filomat, no. 19, pp. 35–44, 2005. View at Zentralblatt MATH