Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 14737, 11 pages
http://dx.doi.org/10.1155/2007/14737
Research Article

Statistical Convergence of Double Sequences on Probabilistic Normed Spaces

Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop 57000, Turkey

Received 7 November 2006; Accepted 26 April 2007

Academic Editor: Rodica D. Costin

Copyright © 2007 S. Karakus and K. Demırcı. 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, no. 12, pp. 535–537, 1942. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. G. Constantin and I. Istrăţescu, Elements of Probabilistic Analysis with Applications, vol. 36 of Mathematics and Its Applications (East European Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989. View at Zentralblatt MATH · View at MathSciNet
  3. B. Schweizer and A. Sklar, “Statistical metric spaces,” Pacific Journal of Mathematics, vol. 10, pp. 313–334, 1960. View at Zentralblatt MATH · View at MathSciNet
  4. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland, New York, NY, USA, 1983. View at Zentralblatt MATH · View at MathSciNet
  5. S. Karakus, “Statistical convergence on probabilistic normed spaces,” Mathematical Communications, vol. 12, pp. 11–23, 2007.
  6. A. Aghajani and K. Nourouzi, “Convex sets in probabilistic normed spaces,” Chaos, Solitons & Fractals, 2006. View at Publisher · View at Google Scholar
  7. H. Steinhaus, “Sur la convergence ordinaire et la convergence asymptotique,” Colloquium Mathematicum, vol. 2, pp. 73–74, 1951.
  8. H. Fast, “Sur la convergence statistique,” Colloquium Mathematicum, vol. 2, pp. 241–244, 1951. View at Zentralblatt MATH · View at MathSciNet
  9. J. S. Connor, “The statistical and strong p-Cesàro convergence of sequences,” Analysis, vol. 8, no. 1-2, pp. 47–63, 1988. View at Zentralblatt MATH · View at MathSciNet
  10. J. S. Connor, “A topological and functional analytic approach to statistical convergence,” in Analysis of Divergence (Orono, Me, 1997), Appl. Numer. Harmon. Anal., pp. 403–413, Birkhäuser, Boston, Mass, USA, 1999. View at Zentralblatt MATH · View at MathSciNet
  11. J. A. Fridy, “On statistical convergence,” Analysis, vol. 5, no. 4, pp. 301–313, 1985. View at Zentralblatt MATH · View at MathSciNet
  12. A. Pringsheim, “Zur theorie der zweifach unendlichen zahlenfolgen,” Mathematische Annalen, vol. 53, no. 3, pp. 289–321, 1900. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Christopher, “The asymptotic density of some k-dimensional sets,” The American Mathematical Monthly, vol. 63, no. 6, pp. 399–401, 1956. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Mursaleen and O. H. H. Edely, “Statistical convergence of double sequences,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 223–231, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. F. Móricz, “Statistical convergence of multiple sequences,” Archiv der Mathematik, vol. 81, no. 1, pp. 82–89, 2003. View at Zentralblatt MATH · View at MathSciNet