Table of Contents
International Journal of Analysis
Volume 2013, Article ID 126163, 7 pages
http://dx.doi.org/10.1155/2013/126163
Research Article

On a New I-Convergent Double-Sequence Space

Department of Mathematics, A.M.U., Aligarh 202002, India

Received 26 November 2012; Revised 17 January 2013; Accepted 18 January 2013

Academic Editor: Wen Xiu Ma

Copyright © 2013 Vakeel A. Khan and Nazneen Khan. 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. K. Vakeel and S. Tabassum, “On some new double sequence spaces of invariant means defined by Orlicz functions,” Communications de la Faculté des Sciences de l'Université d'Ankara Séries A, vol. 60, no. 2, pp. 11–21, 2011. View at Google Scholar · View at MathSciNet
  2. E. D. Habil, “Double sequences and double series,” The Islamic University Journal, Series of Natural Studies and Engineering, vol. 14, pp. 1–32, 2006. View at Google Scholar
  3. M. Mursaleen, “On some new invariant matrix methods of summability,” The Quarterly Journal of Mathematics, vol. 34, no. 133, pp. 77–86, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Banach, Theorie des Operations Lineaires, Warszawa, Poland, 1932.
  5. 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
  6. M. Mursaleen, “Matrix transformations between some new sequence spaces,” Houston Journal of Mathematics, vol. 9, no. 4, pp. 505–509, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. V. A. Khan, “On a new sequence space defined by Orlicz functions,” Communications de la Faculté des Sciences de l'Université d'Ankara Séries A, vol. 57, no. 2, pp. 25–33, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Mursaleen and S. A. Mohiuddine, “Some new double sequence spaces of invariant means,” Glasnik Matematički, vol. 45, no. 1, pp. 139–153, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Z. U. Ahmad and Mursaleen, “An application of Banach limits,” Proceedings of the American Mathematical Society, vol. 103, no. 1, pp. 244–246, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Mursaleen and A. Alotaibi, “On I-convergence in random 2-normed spaces,” Mathematica Slovaca, vol. 61, no. 6, pp. 933–940, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. Mursaleen, S. A. Mohiuddine, and O. H. H. Edely, “On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 603–611, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Mursaleen and S. A. Mohiuddine, “On ideal convergence of double sequences in probabilistic normed spaces,” Mathematical Reports, vol. 12, no. 4, pp. 359–371, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Mursaleen and S. A. Mohiuddine, “On ideal convergence in probabilistic normed spaces,” Mathematica Slovaca, vol. 62, no. 1, pp. 49–62, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. M. Mursaleen, A. Alotaibi, and M. A. Alghamdi, “I-summability and I-approximation through invariant mean,” Journal of Computational Analysis and Applications, vol. 14, no. 6, pp. 1049–1058, 2012. View at Google Scholar · View at MathSciNet
  15. R. A. Raimi, “Invariant means and invariant matrix methods of summability,” Duke Mathematical Journal, vol. 30, pp. 81–94, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. 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
  17. E. Savas and B. E. Rhoades, “On some new sequence spaces of invariant means defined by Orlicz functions,” Mathematical Inequalities & Applications, vol. 5, no. 2, pp. 271–281, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. A. K. Vakeel, K. Ebadullah, and S. Suantai, “On a new I-convergent sequence space,” Analysis, vol. 32, no. 3, pp. 199–208, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. K. Vakeel and K. Ebadullah, “On some I-Convergent sequence spaces defined by a modullus function,” Theory and Applications of Mathematics and Computer Science, vol. 1, no. 2, pp. 22–30, 2011. View at Google Scholar
  20. A. K. Vakeel and K. Ebadullah, “I-convergent difference sequence spaces defined by a sequence of moduli,” Journal of Mathematical and Computational Science, vol. 2, no. 2, pp. 265–273, 2012. View at Google Scholar · View at MathSciNet
  21. A. Komisarski, “Pointwise I-convergence and I-convergence in measure of sequences of functions,” Journal of Mathematical Analysis and Applications, vol. 340, no. 2, pp. 770–779, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  22. V. Kumar, “On I and I-convergence of double sequences,” Mathematical Communications, vol. 12, no. 2, pp. 171–181, 2007. View at Google Scholar · View at MathSciNet
  23. A. Şahiner, M. Gürdal, S. Saltan, and H. Gunawan, “Ideal convergence in 2-normed spaces,” Taiwanese Journal of Mathematics, vol. 11, no. 5, pp. 1477–1484, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. P. Kostyrko, T. Šalát, and W. Wilczyński, “I-convergence,” Real Analysis Exchange, vol. 26, no. 2, pp. 669–685, 2000. View at Google Scholar · View at MathSciNet
  25. T. Šalát, B. C. Tripathy, and M. Ziman, “On some properties of I-convergence,” Tatra Mountains Mathematical Publications, vol. 28, pp. 279–286, 2004. View at Google Scholar · View at MathSciNet
  26. T. Šalát, B. C. Tripathy, and M. Ziman, “On I-convergence field,” Italian Journal of Pure and Applied Mathematics, no. 17, pp. 45–54, 2005. View at Google Scholar · View at MathSciNet
  27. B. C. Tripathy and B. Hazarika, “Paranorm I-convergent sequence spaces,” Mathematica Slovaca, vol. 59, no. 4, pp. 485–494, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  28. V. A. Khan and K. Ebadullah, “On a new difference sequence space of invariant means defined by Orlicz functions,” Bulletin of the Allahabad Mathematical Society, vol. 26, no. 2, pp. 259–272, 2011. View at Google Scholar · View at MathSciNet
  29. A. K. Vakeel and T. Sabiha, “On ideal convergent difference double sequence spaces in 2-normed spaces defined by Orlicz function,” JMI International Journal of Mathematical Sciences, vol. 1, no. 2, pp. 1–9, 2010. View at Google Scholar
  30. P. Das, P. Kostyrko, W. Wilczyński, and P. Malik, “I and I-convergence of double sequences,” Mathematica Slovaca, vol. 58, no. 5, pp. 605–620, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  31. M. Gurdal and M. B. Huban, “On I-convergence of double sequences in the topology induced by random 2-norms,” Matematički Vesnik, vol. 65, no. 3, pp. 1–13, 2013. View at Google Scholar
  32. M. Gürdal and A. Şahiner, “Extremal I-limit points of double sequences,” Applied Mathematics E-Notes, vol. 8, pp. 131–137, 2008. View at Google Scholar · View at MathSciNet
  33. S. Roy, “Some new type of fuzzy I-convergent double difference sequence spaces,” International Journal of Soft Computing and Engineering, vol. 1, pp. 429–431, 2012. View at Google Scholar
  34. I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, 1970. View at MathSciNet
  35. H. Nakano, “Concave modulars,” Journal of the Mathematical Society of Japan, vol. 5, pp. 29–49, 1953. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet