Table of Contents Author Guidelines Submit a Manuscript
International Journal of Analysis
Volume 2014, Article ID 631301, 7 pages
http://dx.doi.org/10.1155/2014/631301
Research Article

Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function

1School of Mathematics and Computer Applications, Thapar University, Patiala, Punjab 147004, India
2Department of Mathematics, Haryana College of Technology and Management, Kaithal, Haryana 136027, India

Received 15 February 2014; Accepted 9 May 2014; Published 28 May 2014

Academic Editor: Shamsul Qamar

Copyright © 2014 Sudhir Kumar 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.

Linked References

  1. P. Schaefer, “Infinite matrices and invariant means,” Proceedings of the American Mathematical Society, vol. 36, pp. 104–110, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  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. Mursaleen, A. K. Gaur, and T. A. Chishti, “On some new sequence spaces of invariant means,” Acta Mathematica Hungarica, vol. 75, no. 3, pp. 209–214, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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 · View at MathSciNet
  5. H. Fast, “Sur la convergence statistique,” Colloquium Mathematicum, vol. 2, pp. 241–244, 1951. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. S. Connor, “The statistical and strong p-Cesàro convergence of sequences,” Analysis. International Mathematical Journal of Analysis and its Applications, vol. 8, no. 1-2, pp. 47–63, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. A. Fridy, “On statistical convergence,” Analysis, vol. 5, no. 4, pp. 301–313, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. I. J. Maddox, “Statistical convergence in a locally convex space,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104, no. 1, pp. 141–145, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. Šalát, “On statistically convergent sequences of real numbers,” Mathematica Slovaca, vol. 30, no. 2, pp. 139–150, 1980. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. R. Freedman, J. J. Sember, and R. Raphael, “Some p-Cesàro type summability spaces,” Proceedings of the London Mathematical Society, vol. 37, no. 2, pp. 508–529, 1978. View at Google Scholar
  11. J. A. Fridy and C. Orhan, “Lacunary statistical convergence,” Pacific Journal of Mathematics, vol. 160, no. 1, pp. 43–51, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. A. Fridy and C. Orhan, “Lacunary statistical summability,” Journal of Mathematical Analysis and Applications, vol. 173, no. 2, pp. 497–504, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. S. Pehlivan and B. Fisher, “Lacunary strong convergence with respect to a sequence of modulus functions,” Commentationes Mathematicae Universitatis Carolinae, vol. 36, no. 1, pp. 69–76, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Et and A. Gökhan, “Lacunary strongly almost summable sequences,” Studia. Universitatis Babeş-Bolyai. Mathematica, vol. 53, no. 4, pp. 29–38, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. B. C. Tripathy and H. Dutta, “On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary Δmn-statistical convergence,” Analele Stiintifice ale Universitatii Ovidius Constanta, vol. 20, no. 1, pp. 417–430, 2012. View at Google Scholar · View at MathSciNet
  16. V. Karakaya, “Some new sequence spaces defined by a sequence of Orlicz functions,” Taiwanese Journal of Mathematics, vol. 9, no. 4, pp. 617–627, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. Kostyrko, T. Šalát, and W. Wilczyński, “I-convergence,” Real Analysis Exchange, vol. 26, no. 2, pp. 669–686, 2000. View at Google Scholar · View at MathSciNet
  18. P. Das, E. Savas, and S. Kr. Ghosal, “On generalizations of certain summability methods using ideals,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1509–1514, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H. Kızmaz, “On certain sequence spaces,” Canadian Mathematical Bulletin, vol. 24, no. 2, pp. 169–176, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. Et and R. Çolak, “On some generalized difference sequence spaces,” Soochow Journal of Mathematics, vol. 21, no. 4, pp. 377–386, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. A. Bakery, E. A. E. Mohamed, and M. A. Ahmed, “Some generalized difference sequence spaces defined by ideal convergence and Musielak-Orlicz function,” Abstract and Applied Analysis, vol. 2013, Article ID 972363, 9 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Başarir, Ş. Konca, and E. E. Kara, “Some generalized difference statistically convergent sequence spaces in 2-normed space,” Journal of Inequalities and Applications, vol. 2013, article 177, pp. 1–10, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  23. V. K. Bhardwaj and S. Gupta, “Cesàro summable difference sequence space,” Journal of Inequalities and Applications, vol. 2013, article 315, pp. 1–9, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. M. Et and M. Basarir, “On some new generalized difference sequence spaces,” Periodica Mathematica Hungarica, vol. 35, no. 3, pp. 169–175, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. Et and A. Bektaş, “Generalized strongly (V,λ)-summable sequences defined by Orlicz functions,” Mathematica Slovaca, vol. 54, no. 4, pp. 411–422, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. M. Et, Y. Altin, and H. Altinok, “On some generalized difference sequence spaces defined by a modulus function,” Filomat, no. 17, pp. 23–33, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. B. Hazarika and A. Esi, “On some I-convergent generalized difference lacunary double sequence spaces defined by orlicz functions,” Acta Scientiarum: Technology, vol. 35, no. 3, pp. 527–537, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Nakano, “Concave modulars,” Journal of the Mathematical Society of Japan, vol. 5, pp. 29–49, 1953. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. W. H. Ruckle, “FK spaces in which the sequence of coordinate vectors is bounded,” Canadian Journal of Mathematics. Journal Canadien de Mathématiques, vol. 25, pp. 973–978, 1973. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. 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 · View at MathSciNet
  31. M. Et, “Spaces of Cesaro difference sequences of order r defined by a modulus function in a locally convex space,” Taiwanese Journal of Mathematics, vol. 10, no. 4, pp. 865–879, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. E. Savas, “On some generalized sequence spaces defined by a modulus,” Indian Journal of Pure and Applied Mathematics, vol. 30, no. 5, pp. 459–464, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. S. Kumar, V. Kumar, and S. S. Bhatia, “Generalized sequence spaces in 2-normed spaces defined by ideal and a modulus function,” Analele Stiintifice ale Universitatii Alexandruioan Cuza din Iasi-Serie Noua- Mathematica. In press.