Main Article Content

Abstract

By using modulus functions, we have obtained a generalization of statistical convergence of asymptotically equivalent sequences, a new non-matrix convergence method, which is intermediate between the ordinary convergence and the statistical convergence. Further, we have examined some inclusion relations related to this concept.

Keywords

statistical convergence strong Cesaro summability sequence space modulus function asymptotically equivalent sequences

Article Details

Author Biography

Sukran Konca, Bitlis Eren University

Department of mathematics
How to Cite
Konca, S., & Kucukaslan, M. (2018). On Asymptotically f-Statistical Equivalent Sequences. Journal of the Indonesian Mathematical Society, 24(2), 54–61. https://doi.org/10.22342/jims.24.2.531.54-61

References

  1. bibitem{aizpuru} Aizpuru, A., Listan-Garcia M.C. and Rambla-Barreno, F., "Density by moduli and statistical convergence", {em Quaestiones Mathematicae.}, textbf{ 37 4} (2014) 525 - 530.
  2. bibitem{bhardwaj} Bhardwaj V.K. and Dhawan, S., "$f$-statistical convergence of order $/alpha$ and strong Cesaro summability of order with respect to a modulus", {em J. Ineq. Appl.}, textbf{ 2015 332} (2015) 14 pages.
  3. bibitem{bdg} Bhardwaj, V.K., Dhawan, S. and Gupta, S., "Density by moduli and statistical boundedness", {em Abst. Appl. Analysis}, textbf{ 2016} Article ID 2143018, 6 pages, 2016.
  4. bibitem{b} Bhardwaj, V.K. and Dhawan, S., "Density by moduli and lacunary statistical convergence", {em Abst. Appl. Analysis}, textbf{ 2016} (2016) Article ID 9365037, 11 pages. http://dx.doi.org/10.1155/2016/9365037
  5. bibitem{tunay} Bilgin, T., "$(sigma,f)$-Asymptotically lacunary equivalent sequences", {em International J. Analysis}, textbf{ 2014} (2014) Article ID 945902, 8 pages. http://dx.doi.org/10.1155/2014/945902
  6. bibitem{fast} Fast, H., "Sur la convergence statistique", {em Colloq. Math.}, textbf{ 2 3-4} (1951) 241--244.
  7. bibitem{maddox} Maddox, I.J., "Sequence spaces defined by a modulus", {em Math. Proc. Camb. Philos. Soc.}, textbf{ 101} (1987) 523 - 527.
  8. bibitem{marouf} Marouf, M., "Asymptotic equivalence and summability", {em Internat. J. Math. Math. Sci.}, textbf{ 16 4} (1993) 755 - 762.
  9. bibitem{nakano} Nakano, H., "Concave modulars", {em J. Math. Soc. Japan}, textbf{ 5} (1953) 29–-49.
  10. bibitem{niven} Niven, I., Zuckerman, H.S. and Montgomery, H.L., {it An introduction to the theory of numbers}, Fifth Ed., John Wiley and Sons, New York, 1991.
  11. bibitem{rfp} Patterson, R.F., "On asymptotically statistically equivalent sequences", {em Demonstratio Math.}, textbf{ 36 1} (2003) 149 - 153.
  12. bibitem{patsav} Patterson R.F. and Savac{s}, E., "On asymptotically lacunary statistically equivalent sequences", {em Thai J. Math.}, textbf{ 4} (2006) 267 - 272.
  13. bibitem{ruckle} Ruckle, W.H., "FK spaces in which the sequence of coordinate vectors is bounded", {em Can. J. Math.}, textbf{ 25} (1973) 973 - 978.
  14. bibitem{schoenberg} Schoenberg, I.J., "The integrability of certain functions and related summability methods", {em Amer. Math. Monthly.}, textbf{ 66 5} (1959) 361 - 375.
  15. bibitem{seneta} Seneta, E., {it Regularly varying functions}, Lecture Notes in Mathematics {bf 508} Springer-Verlag, Berlin-Heidelberg-New York, 1976.
  16. bibitem{steinhaus} Steinhaus, H., "Sur la convergence ordinaire et la convergence asymptotique", {em Colloq. Math.}, textbf{ 2 1} (1951) 73 - 74.