Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 189721, 5 pages
http://dx.doi.org/10.1155/2013/189721
Research Article

Lacunary Statistical Limit Points in Random 2-Normed Spaces

Department of Mathematics, Suleyman Demirel University, 32260 Isparta, Turkey

Received 29 April 2013; Accepted 13 June 2013

Academic Editors: F. Colombini and J.-L. Wu

Copyright © 2013 A. Güncan 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. K. Menger, “Statistical metrics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 28, pp. 535–537, 1942. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, NY, USA, 1983. View at MathSciNet
  3. I. Goleţ, “On probabilistic 2-normed spaces,” Novi Sad Journal of Mathematics, vol. 35, no. 1, pp. 95–102, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Gähler, “2-metrische Räume und ihre topologische Struktur,” Mathematische Nachrichten, vol. 26, pp. 115–148, 1963. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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
  6. M. Mursaleen, “On statistical convergence in random 2-normed spaces,” Acta Scientiarum Mathematicarum, vol. 76, no. 1-2, pp. 101–109, 2010. View at Google Scholar · View at MathSciNet
  7. 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
  8. H. Fast, “Sur la convergence statistique,” Colloquium Mathematicae, vol. 2, pp. 241–244, 1951. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Steinhaus, “Sur la convergence ordinaire et la convergence asymptotique,” Colloquium Mathematicum, vol. 2, pp. 73–74, 1951. View at Google Scholar
  10. T. Salat, “On statistical convergence of real numbers,” Mathematica Slovaca, vol. 50, pp. 111–115, 2000. View at Google Scholar
  11. J. A. Fridy, “On statistical convergence,” Analysis, vol. 5, no. 4, pp. 301–313, 1985. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. 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 MathSciNet
  13. M. Mursaleen and S. A. Mohiuddine, “On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 142–149, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. A. Mohiuddine and E. Savaş, “Lacunary statistically convergent double sequences in probabilistic normed spaces,” Annali dell'Universitá di Ferrara, vol. 58, no. 2, pp. 331–339, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. S. Gähler, “Lineare 2-normierte Räume,” Mathematische Nachrichten, vol. 28, pp. 1–43, 1964. View at Publisher · View at Google Scholar · View at MathSciNet
  16. J. A. Fridy, “Statistical limit points,” Proceedings of the American Mathematical Society, vol. 118, no. 4, pp. 1187–1192, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. A. Fridy and C. Orhan, “Lacunary statistical convergence,” Pacific Journal of Mathematics, vol. 160, no. 1, pp. 43–51, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet