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Abstract and Applied Analysis
Volume 2014, Article ID 818020, 5 pages
http://dx.doi.org/10.1155/2014/818020
Research Article

Invariant Statistical Convergence of Sequences of Sets with respect to a Modulus Function

Department of Mathematics, Afyon Kocatepe University, Afyonkarahisar, Turkey

Received 15 December 2013; Accepted 21 February 2014; Published 23 March 2014

Academic Editor: Irena Rachůnková

Copyright © 2014 Nimet Pancaroglu and Fatih Nuray. 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. Fast, “Sur la convergence statistique,” Colloquium Mathematicae, vol. 2, no. 3-4, pp. 241–244, 1951. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. 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 Zentralblatt MATH · View at MathSciNet
  3. G. Beer, “Convergence of continuous linear functionals and their level sets,” Archiv der Mathematik, vol. 52, no. 5, pp. 482–491, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. P. Aubin and H. Frankowska, Set Valued Analysis, Birkhäuser, Boston, Mass, USA, 1990. View at MathSciNet
  5. M. Baronti and P. L. Papini, “Convergence of sequences of sets,” in Methods of Functional Analysis in Approximation Theory, vol. 76, pp. 135–155, Birkhäuser, Basel, Switzerland, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. Nuray and B. E. Rhoades, “Statistical convergence of sequences of sets,” Fasciculi Mathematici, no. 49, pp. 87–99, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. U. Ulusu and F. Nuray, “Lacunary statistical convergence sequences of sets,” Progress in Applied Mathematics, vol. 4, no. 2, pp. 99–109, 2012. View at Google Scholar
  8. N. Pancaroglu and F. Nuray, “On invariant statistically convergence and lacu-nary invariant statistically convergence of sequences of sets,” Progress in Applied Mathematics, vol. 5, no. 2, pp. 23–29, 2013. View at Google Scholar
  9. H. Nakano, “Concave modulars,” Journal of the Mathematical Society of Japan, vol. 5, no. 1, pp. 29–49, 1953. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. H. Ruckle, “FK spaces in which the sequence of coordinate vectors is bounded,” Canadian Journal of Mathematics, vol. 25, pp. 973–978, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. I. J. Maddox, “Sequence spaces defined by a modulus,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 100, no. 1, pp. 161–166, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Connor, “On strong matrix summability with respect to a modulus and statistical convergence,” Canadian Mathematical Bulletin, vol. 32, no. 2, pp. 194–198, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. F. Nuray and E. Savaş, “Some new sequence spaces defined by a modulus function,” Indian Journal of Pure and Applied Mathematics, vol. 24, no. 11, pp. 657–663, 1993. View at Google Scholar · View at MathSciNet
  14. E. Savaş, “Strongly σ-convergent sequences,” Bulletin of the Calcutta Mathematical Society, vol. 81, no. 4, pp. 295–300, 1989. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. E. Savaş, “On strong almost A-summability with respect to a modulus and statistical convergence,” Indian Journal of Pure and Applied Mathematics, vol. 23, no. 3, pp. 217–222, 1992. View at Google Scholar · View at MathSciNet