Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 858504, 8 pages
http://dx.doi.org/10.1155/2014/858504
Research Article

Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces

1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Model Institute of Engineering & Technology, Kot Bhalwal 181122, India

Received 29 March 2014; Accepted 28 June 2014; Published 24 July 2014

Academic Editor: Hassan Eltayeb

Copyright © 2014 M. Mursaleen 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. J. Lindenstrauss and L. Tzafriri, “On Orlicz sequence spaces,” Israel Journal of Mathematics, vol. 10, pp. 379–390, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Mathematics 5, Polish Academy of Science, 1989.
  3. J. Musielak, Orlicz Spaces and Modular Spaces, vol. 1034 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1983. View at MathSciNet
  4. A. Wilansky, Summability through Functional Analysis, vol. 85, North-Holland, Amsterdam, Netherlands, 1984. View at MathSciNet
  5. M. Mursaleen and A. K. Noman, “On some new sequence spaces of non absolute type related to the spaces lp and l II,” Mathematical Communications, vol. 16, pp. 383–398, 2011. View at Google Scholar
  6. S. D. Parashar and B. Choudhary, “Sequence spaces defined by Orlicz functions,” Indian Journal of Pure and Applied Mathematics, vol. 25, no. 4, pp. 419–428, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. K. Raj and S. K. Sharma, “Some sequence spaces in 2-normed spaces defined by Musielak-Orlicz function,” Acta Universitatis Sapientiae: Mathematica, vol. 3, no. 1, pp. 97–109, 2011. View at Google Scholar · View at MathSciNet
  8. K. Raj and S. K. Sharma, “Some generalized difference double sequence spaces defined by a sequence of Orlicz-functions,” Cubo, vol. 14, no. 3, pp. 167–189, 2012. View at Google Scholar · View at MathSciNet
  9. K. Raj and S. K. Sharma, “Some multiplier sequence spaces defined by a Musielak-Orlicz function in n-normed spaces,” New Zealand Journal of Mathematics, vol. 42, pp. 45–56, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Gökhan, 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 MathSciNet · View at Scopus
  11. M. Gungor and M. Et, “ΔT-strongly almost summable sequences defined by Orlicz functions,” Indian Journal of Pure and Applied Mathematics, vol. 34, no. 8, pp. 1141–1151, 2003. View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. R. Freedman, J. J. Sember, and M. Raphael, “Some Cesàro-type summability spaces,” Proceedings of the London Mathematical Society, vol. 37, no. 3, pp. 508–520, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  13. T. Bilgin, “Lacunary strong A-convergence with respect to a modulus,” Studia Universitatis Babeş-Bolyai, vol. 46, no. 4, pp. 39–46, 2001. View at Google Scholar · View at MathSciNet
  14. T. Bilgin, “Lacunary strong A-convergence with respect to a sequence of modulus functions,” Applied Mathematics and Computation, vol. 151, no. 3, pp. 595–600, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Mursaleen and A. K. Noman, “On some new sequence spaces of non-absolute type related to the spaces lp and l I,” Filomat, vol. 25, no. 2, pp. 33–51, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. H. Fast, “Sur la convergence statistique,” Colloquium Mathematicae, vol. 2, pp. 241–244, 1951. View at Google Scholar · View at MathSciNet
  17. I. J. Schoenberg, “The integrability of certain functions and related summability methods,” The American Mathematical Monthly, vol. 66, pp. 361–375, 1959. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. A. Fridy, “On statistical convergence,” Analysis, vol. 5, no. 4, pp. 301–313, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  19. J. S. Connor, “A topological and functional analytic approach to statistical convergence,” in Applied and Numerical Harmonic Analysis, vol. 8 of Analysis of Divergence, pp. 403–413, 1999. View at Google Scholar
  20. 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 MathSciNet
  21. M. Mursaleen and O. H. H. Edely, “Generalized statistical convergence,” Information Sciences, vol. 162, no. 3-4, pp. 287–294, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. M. Isk, “On statistical convergence of generalized difference sequences,” Soochow Journal of Mathematics, vol. 30, no. 2, pp. 197–205, 2004. View at Google Scholar · View at MathSciNet
  23. S. A. Mohiuddine and M. A. Alghamdi, “Statistical summability through a lacunary sequence in locally solid Riesz spaces,” Journal of Inequalities and Applications, vol. 2012, article 225, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. B. Hazarika, S. A. Mohiuddine, and M. Mursaleen, “Some inclusion results for lacunary statistical convergence in locally solid Riesz spaces,” Iranian Journal of Science Technology, vol. 38, no. A1, pp. 61–68, 2014. View at Google Scholar
  25. E. Kolk, “The statistical convergence in Banach spaces,” Acta et Commentationes Universitatis Tartuensis, vol. 928, pp. 41–52, 1991. View at Google Scholar · View at MathSciNet
  26. 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
  27. A. Alotaibi and M. Mursaleen, “Statistical convergence in random paranormed space,” Journal of Computational Analysis and Applications, vol. 17, no. 2, pp. 297–304, 2014. View at Google Scholar · View at MathSciNet
  28. S. A. Mohiuddine, K. Raj, and A. Alotaibi, “Some paranormed double difference sequence spaces for Orlicz functions and bounded-regular matrices,” Abstract and Applied Analysis, vol. 2014, Article ID 419064, 10 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  29. S. A. Mohiuddine and M. Aiyub, “Lacunary statistical convergence in random 2-normed spaces,” Applied Mathematics & Information Sciences, vol. 6, no. 3, pp. 581–585, 2012. View at Google Scholar · View at Scopus