DOI QR코드

DOI QR Code

On Deferred Statistical Convergence of Sequences

Kucukaslan, Mehme;Yilmazturk, Mujde

  • Received : 2012.09.26
  • Accepted : 2016.03.28
  • Published : 2016.06.23

Abstract

In this paper, deferred statistical convergence is defined by using deferred $Ces{\grave{a}}ro$ mean instead of $Ces{\grave{a}}ro$ mean in the definition of statistical convergence. The obtained method is compared with strong deferred $Ces{\grave{a}}ro$ mean and statistical convergence under some certain assumptions. Also, some inclusion theorems and examples are given.

Keywords

statistical convergence;deferred statistical convergence;summability of sequences;strongly summability

References

  1. R. P. Agnew, On deferred Cesaro Mean, Comm. Ann. Math., 33(1932), 413-421. https://doi.org/10.2307/1968524
  2. R. C. Buck, Generalized asymptotic density, Amer. J. Math., 75(1953), 335-346. https://doi.org/10.2307/2372456
  3. J. S. Connor, The statistical and strong p-Cesaro of sequences, Analysis, 8(1988), 47-63.
  4. J. S. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(1989), 194-198. https://doi.org/10.4153/CMB-1989-029-3
  5. P. Erdos and G. Tenenbaum, Sur les densites de certaines suites d'entiers, Proc. London Math. Soc., 59(3)(1989), 417-438.
  6. H. Fast, Sur la convergence statiistique, Colloq. Math., 2(1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  7. A. R. Freedman, J. J. Sember and M. aphael, Some Cesarotype summability spaces, Proc. London Math.soc., 37(1978), 301-313.
  8. J. A Fridy, On statistical convergence, Analysis, 5(1985), 301-313.
  9. J. A. Fridy, and C. Orhan, Lacunary statistical convergence, Pacific. J. Math., 160(1993), 43-51. https://doi.org/10.2140/pjm.1993.160.43
  10. J. A. Fridy and H. I.Miller, A matrix characterization of statistical convergence, Analysis, 11(1991), 59-66.
  11. I. J. Maddox, Elements of Functional Analysis, Cambridge at the University Press, (1970).
  12. I. J. Maddox, Space of strongly summable functions, Oxford(2), Quart. J. Mah., (1967), 345-355.
  13. M. Mursaleen, ${\lambda}$-statistical convergence, Math. Slovaca, 50(1)(2000), 111-115.
  14. F. Nuray, ${\lambda}$-strongly summable and ${\lambda}$- statistically convergencet functions, Iran. J. Sci. Technol. Trans. A Sci., 34(A4)(2010), 335-338.
  15. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30(1980), 139-150.
  16. I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(1959), 361-375. https://doi.org/10.2307/2308747
  17. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1951), 73-74.
  18. J. A. Osikiewicz, Summability of Matrix Submethods and Spliced Sequences, Ph.D. Thesis, August, (1997).
  19. A. Zygmund, Trigonometric Series, Cambiridge Univ. Press Cambridge, U. K., (1979).

Cited by

  1. in Amenable Semigroups vol.13, pp.2271-2097, 2017, https://doi.org/10.1051/itmconf/20171301004