Skip to main content
SpringerLink
Log in

On statistical convergence of vector-valued sequences associated with multiplier sequences

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We introduce vector-valued sequence spaces w ∞(F, Q, p, u), w 1(F, Q, p, u), w 0(F, Q, p, u), S q u , and S q0u using a sequence of modulus functions and a multiplier sequence u = (u k ) of nonzero complex numbers. We give some relations for these sequence spaces. It is also shown that if a sequence is strongly u q -Cesàro summable with respect to the modulus function, then it is u q -statistically convergent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Rath and P. D. Srivastava, “On some vector valued sequence spaces ℓ (p)∞ (E k , Λ),” Ganita, 47, No. 1, 1–12 (1996).

    MathSciNet  Google Scholar 

  2. N. R. Das and A. Choudhary, “Matrix transformation of vector valued sequence spaces,” Bull. Calcutta Math. Soc., 84, 47–54 (1992).

    MathSciNet  MATH  Google Scholar 

  3. I. E. Leonard, “Banach sequence spaces,” J. Math. Anal. Appl., 54, 245–265 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  4. J. K. Srivastava and B. K. Srivastava, “Generalized sequence space c 0(X, λ, p),” Indian J. Pure Appl. Math., 27, No. 1, 73–84 (1996).

    MathSciNet  MATH  Google Scholar 

  5. B. C. Tripathy and M. Sen, “Vector valued paranormed bounded and null sequence spaces associated with multiplier sequences,” Soochow J. Math., 29, No. 4, 379–391 (2003).

    MathSciNet  MATH  Google Scholar 

  6. B. C. Tripathy and S. Mahanta, “On a class of vector valued sequences associated with multiplier sequences,” Acta Math. Appl. Sinica (to appear).

  7. R. Çolak, “On invariant sequence spaces,” Erc. Univ. J. Sci., 5, No. 1–2, 881–887 (1989).

    Google Scholar 

  8. R. Çolak, P. D. Srivastava, and S. Nanda, “On certain sequence spaces and their Köthe-Toeplitz duals,” Rend. Mat. Appl., Ser 13, No. 1, 27–39 (1993).

    Google Scholar 

  9. H. Nakano, “Concave modulars,” J. Math. Soc. Jpn., 5, 29–49 (1953).

    Article  MATH  MathSciNet  Google Scholar 

  10. W. H. Ruckle, “FK spaces in which the sequence of coordinate vectors is bounded,” Can. J. Math., 25, 973–978 (1973).

    MATH  MathSciNet  Google Scholar 

  11. I. J. Maddox, “Sequence spaces defined by a modulus,” Math. Proc. Cambridge Phil. Soc., 100, 161–166 (1986).

    MATH  MathSciNet  Google Scholar 

  12. I. J. Maddox, “On strong almost convergence,” Math. Proc. Cambridge Phil. Soc., 85, 161–166 (1979).

    MathSciNet  Google Scholar 

  13. H. Fast, “Sur la convergence statistique,” Colloq. Math., 2, 241–244 (1951).

    MATH  MathSciNet  Google Scholar 

  14. I. J. Schoenberg, “The integrability of certain functions and related summability methods,” Amer. Math. Monthly, 66, 361–375 (1959).

    Article  MATH  MathSciNet  Google Scholar 

  15. J. A. Fridy, “On the statistical convergence,” Analysis, 5, 301–313 (1985).

    MATH  MathSciNet  Google Scholar 

  16. J. S. Connor, “A topological and functional analytic approach to statistical convergence,” Appl. Numer. Harmonic Anal., 403–413 (1999).

  17. T. Šalàt, “On statistically convergent sequences of real numbers,” Math. Slovaca, 30, No. 2, 139–150 (1980).

    MathSciNet  MATH  Google Scholar 

  18. Mursaleen, “λ-Statistical convergence,” Math. Slovaca, 50, 111–115 (2000).

    MathSciNet  MATH  Google Scholar 

  19. M. Isik, “On statistical convergence of generalized difference sequences,” Soochow J. Math., 30, No. 2, 197–205 (2004).

    MATH  MathSciNet  Google Scholar 

  20. E. Savaş, “Strong almost convergence and almost λ-statistical convergence,” Hokkaido Math. J., 29, 531–536 (2000).

    MathSciNet  MATH  Google Scholar 

  21. E. Malkowsky and E. Savaş, “Some λ-sequence spaces defined by a modulus,” Arch. Math., 36, 219–228 (2000).

    MATH  Google Scholar 

  22. E. Kolk, “The statistical convergence in Banach spaces,” Acta. Comment. Univ. Tartu, 928, 41–52 (1991).

    MathSciNet  Google Scholar 

  23. I. J. Maddox, “Statistical convergence in a locally convex space,” Math. Proc. Cambridge Phil. Soc., 104, 141–145 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  24. B. C. Tripathy and M. Sen, “On generalized statistically convergent sequences,” Indian J. Pure Appl. Math., 32, No. 11, 1689–1694 (2001).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fırat University, Elaziğg, Turkey

    M. Et, A. Gökhan & H. Altinok

Authors
  1. M. Et
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Gökhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Altinok
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 125–131, January, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Et, M., Gökhan, A. & Altinok, H. On statistical convergence of vector-valued sequences associated with multiplier sequences. Ukr Math J 58, 139–146 (2006). https://doi.org/10.1007/s11253-006-0056-y

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0056-y

Keywords

Search

Navigation