Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 535419, 5 pages
http://dx.doi.org/10.1155/2014/535419
Research Article

On -Statistical Convergence of Order

1Department of Mathematics, Fırat University, 23119 Elazıg, Turkey
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 31 August 2013; Accepted 6 November 2013; Published 9 February 2014

Academic Editors: H. Bulut, Y. Deng, and K.-L. Hsiao

Copyright © 2014 Mikail Et 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. A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.
  2. H. Steinhaus, “Sur la convergence ordinaire et la convergence asymptotique,” Colloquium Mathematicum, vol. 2, pp. 73–74, 1951. View at Google Scholar
  3. H. Fast, “Sur la convergence statistique,” Colloquium Mathematicum, vol. 2, pp. 241–244, 1951. View at Google Scholar
  4. I. J. Schoenberg, “The integrability of certain functions and related summability methods,” The American Mathematical Monthly, vol. 66, pp. 361–375, 1959. View at Google Scholar
  5. J. S. Connor, “The Statistical and strong p-Cesàro convergence of sequences,” Analysis, vol. 8, pp. 47–63, 1988. View at Google Scholar
  6. M. Çınar, M. Karakaş, and M. Et, “On pointwise and uniform statistical convergence of order for sequence of functions,” Fixed Point Theory and Applications, vol. 2013, article 33, 2013. View at Google Scholar
  7. M. Et, M. C. Çınar, and M. Karakaş, “On λ-statistical convergence of order of sequences of function,” Journal of Inequalities and Applications, vol. 2013, article 204, 2013. View at Google Scholar
  8. J. A. Fridy, “On statistical convergence,” Analysis, vol. 5, pp. 301–313, 1985. View at Google Scholar
  9. M. Güngör, M. Et, and Y. Altin, “Strongly (Vσ,λ,q) -summable sequences defined by Orlicz functions,” Applied Mathematics and Computation, vol. 157, no. 2, pp. 561–571, 2004. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Güngor and M. Et, “Δr-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 Scopus
  11. M. Işik, “Strongly almost (ω, λ, q)-summable sequences,” Mathematica Slovaca, vol. 61, no. 5, pp. 779–788, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Belen and S. A. Mohiuddine, “Generalized weighted statistical convergence and application,” Applied Mathematics and Computation, vol. 219, pp. 9821–9826, 2013. View at Google Scholar
  13. S. A. Mohiuddine, A. Alotaibi, and M. Mursaleen, “Statistical convergence of double sequences in locally solid Riesz spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 719729, 9 pages, 2012. View at Publisher · View at Google Scholar
  14. O. H. H. Edely, S. A. Mohiuddine, and A. K. Noman, “Korovkin type approximation theorems obtained through generalized statistical convergence,” Applied Mathematics Letters, vol. 23, no. 11, pp. 1382–1387, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Mursaleen, “λ-statistical convergence,” Mathematica Slovaca, vol. 50, no. 1, pp. 111–115, 2000. View at Google Scholar
  16. T. Şalàt, “On statistically convergent sequences of real numbers,” Mathematica Slovaca, vol. 30, pp. 139–150, 1980. View at Google Scholar
  17. P. Kostyrko, T. Şalàt, and W. Wilczyński, “I-convergence,” Real Analysis Exchange, vol. 26, pp. 669–686, 2000/2001. View at Google Scholar
  18. F. Nuray and W. H. Ruckle, “Generalized statistical convergence and convergence free spaces,” Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 513–527, 2000. View at Google Scholar · View at Scopus
  19. 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 Scopus
  20. P. Das, E. Savas, and S. K. 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 Scopus
  21. E. Savas and P. Das, “A generalized statistical convergence via ideals,” Applied Mathematics Letters, vol. 24, no. 6, pp. 826–830, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Kostyrko, M. Mačaj, M. Sleziak, and T. Şalàt, “I-convergence and extremal I-limit points,” Mathematica Slovaca, vol. 55, no. 4, pp. 443–464, 2005. View at Google Scholar
  23. B. Hazarika and S. A. Mohiuddine, “Ideal convergence of random variables,” Journal of Function Spaces and Applications, vol. 2013, Article ID 148249, 7 pages, 2013. View at Publisher · View at Google Scholar
  24. S. A. Mohiuddine, A. Alotaibi, and S. M. Alsulami, “Ideal convergence of double sequences in random 2-normed spaces,” Advances in Difference Equations, vol. 2012, article 149, 2012. View at Google Scholar
  25. 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 Scopus
  26. T. Şalàt, B. C. Tripathy, and M. Ziman, “On I-convergence field,” Italian Journal of Pure and Applied Mathematics, vol. 17, pp. 45–54, 2005. View at Google Scholar
  27. T. Şalàt, B. C. Tripathy, and M. Ziman, “On some properties of I-convergence,” Tatra Mountains Mathematical Publications, vol. 28, part II, pp. 279–286, 2004. View at Google Scholar
  28. 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 Scopus
  29. B. C. Tripathy and B. Hazarika, “Some I-convergent sequence spaces defined by Orlicz functions,” Acta Mathematicae Applicatae Sinica, vol. 27, no. 1, pp. 149–154, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. A. D. Gadjiev and C. Orhan, “Some approximation theorems via statistical convergence,” Rocky Mountain Journal of Mathematics, vol. 32, no. 1, pp. 129–138, 2002. View at Google Scholar · View at Scopus
  31. R. Çolak, Statistical Convergence of Order, Modern Methods in Analysis and Its Applications, Anamaya, New Delhi, India, 2010.
  32. H. Kızmaz, “On certain sequence spaces,” Canadian Mathematical Bulletin, vol. 24, no. 2, pp. 169–176, 1981. View at Google Scholar
  33. M. Et, “Strongly almost summable difference sequences of order m defined by a modulus,” Studia Scientiarum Mathematicarum Hungarica, vol. 40, no. 4, pp. 463–476, 2003. View at Publisher · View at Google Scholar · View at Scopus
  34. M. Et, Y. Altin, B. Choudhary, and B. C. Tripathy, “On some classes of sequences defined by sequences of orlicz functions,” Mathematical Inequalities and Applications, vol. 9, no. 2, pp. 335–342, 2006. View at Google Scholar · View at Scopus
  35. M. Et, “Generalized Cesàro difference sequence spaces of non-absolute type involving lacunary sequences,” Applied Mathematics and Computation, vol. 219, no. 17, pp. 9372–9376, 2013. View at Google Scholar
  36. B. Altay and F. Başar, “On the fine spectrum of the difference operator Δ on c0 and c,” Information Sciences, vol. 168, no. 1–4, pp. 217–224, 2004. View at Publisher · View at Google Scholar · View at Scopus
  37. Y. Altin, M. Et, and M. Basarir, “On some generalized difference sequences of fuzzy numbers,” Kuwait Journal of Science and Engineering, vol. 34, no. 1A, pp. 1–14, 2007. View at Google Scholar
  38. R. Çolak, H. Altinok, and M. Et, “Generalized difference sequences of fuzzy numbers,” Chaos, Solitons and Fractals, vol. 40, no. 3, pp. 1106–1117, 2009. View at Publisher · View at Google Scholar · View at Scopus
  39. 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 Scopus
  40. H. Gumus, I-Convergence and asymptotic I-equivalence of difference sequences [Ph.D. thesis], Afyon Kocatepe University, 2011.