Skip to main content
SpringerLink
Log in

On some generalized difference paranormed sequence spaces associated with multiplier sequence defined by modulus function

  • Published:
Analysis in Theory and Applications

Abstract

In this article we introduce the paranormed sequence spaces (f, Λ, Δm, p), c0(f, Λ, Δm, p) and ℓ∞(f, Λ, Δm, p), associated with the multiplier sequence Λ = (λk), defined by a modulus function f. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

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. Bilgin, T., The Sequence Space ℓ(p, f, q, s) on Seminormed Spaces, Bull. Calcutta Math. Soc., (1994), 295–304.

  2. Et, M., Altin, Y., Choudhary, B. and Tripathy, B.C., On Some Classes of Sequences Defined by Sequences of Orlicz Functions, Math. Inequalities Appl., 9:2(2006), 335–342.

    Article  MathSciNet  Google Scholar 

  3. Goes, G. and Goes, S., Sequences of Bounded Variation and Sequences of Fourier Coefficients, Math. Zeift., 118(1970), 93–102.

    Article  MathSciNet  Google Scholar 

  4. Kamthan, P. K., Bases in Certain Class of Frechet Spaces, Tamkang Jour. Math., 7(1976), 41–49.

    MathSciNet  MATH  Google Scholar 

  5. Kizmaz, H., On Certain Sequence Spaces, Canad. Math. Bull., 24:2(1981), 169–176.

    Article  MathSciNet  Google Scholar 

  6. Lascarides, C. G., A Study of Certain Sequence Spaces of Maddox and a Generalization of a Theorem of Iyer, Pacific Jour. Math., 38:2(1971), 487–500.

    Article  MathSciNet  Google Scholar 

  7. Maddox, I. J., Spaces of Strongly Summable Sequences, Quart. Jour. Math. (2nd Ser.), 18(1967), 345–355.

    MathSciNet  MATH  Google Scholar 

  8. Nakano, H., Concave Modulars, J. Math Soc. Japan, 5(1953), 29–49.

    Article  Google Scholar 

  9. Ruckle, W. H., FK Spaces in which the Sequence of Co-ordinate Vectors is Bounded, Canad. Jour. Math., XXV(5)(1973), 973–978.

    Article  Google Scholar 

  10. Simons, S., The Sequence Spaces ℓ(p ν) and m(p ν), Proc. London Math. Soc., 15:3(1965), 422–436.

    Article  MathSciNet  Google Scholar 

  11. Tripathy, B. C., On Generalized Difference Paranormed Statistically Convergent Sequences, Indian Journal of Pure and Applied Mathematics, 35:5(2004), 655–663.

    MathSciNet  MATH  Google Scholar 

  12. Tripathy, B.C. and Esi, A., A New type of Difference Sequence Spaces, International. Journal Sci. Tech., 1:1(2006), 11–14.

    Google Scholar 

  13. Tripathy, B. C. and Sen, M., On Generalized Statistically Convergent Sequences, Indian J. Pure Appl. Math., 32:11(2001), 1689–1694.

    MathSciNet  MATH  Google Scholar 

  14. Tripathy, B. C. and Sen, M., Characterization of Some Matrix Classes Involving Paranormed Sequence Spaces, Tamkang Jour. Math., 37:2(2006), 155–162.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Sciences Division, Institute of Advanced Study in Science and Technology Paschim Baragaon, Garchuk, Guwahati, 781035, India

    Binod Chandra Tripathy

  2. Department of Mathematics, Patna University, Patna, 800005, India

    Prabhat Chandra

Authors
  1. Binod Chandra Tripathy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Prabhat Chandra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Binod Chandra Tripathy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tripathy, B.C., Chandra, P. On some generalized difference paranormed sequence spaces associated with multiplier sequence defined by modulus function. Anal. Theory Appl. 27, 21–27 (2011). https://doi.org/10.1007/s10496-011-0021-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10496-011-0021-y

Key words

AMS (2010) subject classification

Search

Navigation