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International Journal of Mathematics and Mathematical Sciences
Volume 2015, Article ID 984283, 6 pages
http://dx.doi.org/10.1155/2015/984283
Research Article

Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

Department of Mathematics, Bozok University, Yozgat, Turkey

Received 28 April 2015; Accepted 16 June 2015

Academic Editor: Binod C. Tripathy

Copyright © 2015 Ugur Kadak. 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. 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 MathSciNet
  2. M. Et and R. Colak, “On some generalized difference sequence spaces,” Soochow Journal of Mathematics, vol. 21, no. 4, pp. 377–386, 1995. View at Google Scholar · View at MathSciNet
  3. M. Et and A. Esi, “On Köthe-Toeplitz duals of generalized difference sequence spaces,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 23, no. 1, pp. 25–32, 2000. View at Google Scholar · View at MathSciNet
  4. 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 MathSciNet
  5. C. Aydın and F. Başar, “Some new difference sequence spaces,” Applied Mathematics and Computation, vol. 157, no. 3, pp. 677–693, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. Mursaleen, “Generalized spaces of difference sequences,” Journal of Mathematical Analysis and Applications, vol. 203, no. 3, pp. 738–745, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. Mursaleen and A. K. Noman, “On some new difference sequence spaces of non-absolute type,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 603–617, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. E. Malkowsky, M. Mursaleen, and S. Suantai, “The dual spaces of sets of difference sequences of order m and matrix transformations,” Acta Mathematica Sinica (English Series), vol. 23, no. 3, pp. 521–532, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Ç. A. Bektaş, M. Et, and R. Çolak, “Generalized difference sequence spaces and their dual spaces,” Journal of Mathematical Analysis and Applications, vol. 292, no. 2, pp. 423–432, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  10. B. C. Tripathy, Y. Altin, and M. Et, “Generalized difference sequence spaces on seminormed space defined by Orlicz functions,” Mathematica Slovaca, vol. 58, no. 3, pp. 315–324, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. B. C. Tripathy and B. Sarma, “Some classes of difference paranormed sequence spaces defined by Orlicz functions,” Thai Journal of Mathematics, vol. 3, no. 2, pp. 209–218, 2005. View at Google Scholar · View at MathSciNet
  12. 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 · View at MathSciNet
  13. R. Colak, B. C. Tripathy, and M. Et, “Lacunary strongly summable sequences and q-lacunary almost statistical convergence,” Vietnam Journal of Mathematics, vol. 34, no. 2, pp. 129–138, 2006. View at Google Scholar · View at MathSciNet
  14. V. Karakaya, “Some geometric properties of sequence spaces involving lacunary sequence,” Journal of Inequalities and Applications, vol. 2007, Article ID 081028, 8 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Et, “Generalized Cesáro difference sequence spaces of non-absolute type involving lacunary sequences,” Applied Mathematics and Computation, vol. 219, no. 17, pp. 9372–9376, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. S. Shiue, “On the Cesáro sequence space,” Tamkang Journal of Mathematics, vol. 1, no. 1, pp. 19–25, 1970. View at Google Scholar · View at MathSciNet
  17. A. A. Jagers, “A note on Cesáro sequence spaces,” Nieuw Archief voor Wiskunde, vol. 22, no. 3, pp. 113–124, 1974. View at Google Scholar · View at MathSciNet
  18. P. N. Ng and P. Y. Lee, “Cesáro sequence spaces of non-absolute type,” Commentationes Mathematicae, vol. 20, pp. 429–433, 1978. View at Google Scholar
  19. P. N. Ng and P. Y. Lee, “On the associate spaces of Cesáro sequence space,” Nanta Mathematica, vol. 9, no. 2, pp. 168–170, 1976. View at Google Scholar · View at MathSciNet
  20. P. Baliarsingh, “Some new difference sequence spaces of fractional order and their dual spaces,” Applied Mathematics and Computation, vol. 219, no. 18, pp. 9737–9742, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  21. P. Baliarsingh and S. Dutta, “On the classes of fractional order difference sequence spaces and their matrix transformations,” Applied Mathematics and Computation, vol. 250, pp. 665–674, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. U. Kadak and P. Baliarsingh, “On certain Euler difference sequence spaces of fractional order and related dual properties,” The Journal of Nonlinear Science and Applications, vol. 8, pp. 997–1004, 2015. View at Google Scholar
  23. H. Fast, “Sur la convergence statistique,” Colloquium Mathematicum, vol. 2, no. 1, pp. 241–244, 1951. View at Google Scholar
  24. 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