Skip to main content
SpringerLink
Log in

Seminormed approximation by deferred matrix means of integrable functions in \(H_{P}^{(\omega )}\) space

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper we consider some deferred matrix means of Fourier series. We give the degree of seminormed approximation of functions from the spaces \( H_{P}^{(w)}\) space by such matrix means. As a measure of the approximation is used an almost nondecreasing function of the form \(\frac{w}{v}\) with moduli of continuity type w and v.The obtained results generalize and improve the results from Deǧer and Küçükaslan (J. Inequal. Appl., 2015:14 ,16 pp 2015) and Das et al. (J. Math. Anal. Appl. 420(1), 563–575 2014).

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. Agnew, R.P.: The deferred Cesàro means. Ann. of Math. 33(3), 413–421 (1932)

    Article  MathSciNet  Google Scholar 

  2. Aslan, H., Guven, A.: Approximation by nonlinear Fourier basis in generalized Hölder spaces. Sigma J. Eng. & Nat. Sci. 10(2), 135–142 (2019)

    Google Scholar 

  3. Bustamante, J., Roldan, C.C.: Direct and inverse results in Hölder norms. J. Approx. Theory 138(1), 112–123 (2006)

    Article  MathSciNet  Google Scholar 

  4. Das, G., Nayak, L., Ray, B.: An estimate of the rate of convergence of Fourier series in the generalized Hölder metric by deferred Cesàro mean. J. Math. Anal. Appl. 420(1), 563–575 (2014)

    Article  MathSciNet  Google Scholar 

  5. Deǧer, U., Bayindir, H.: On the degree of approximation by the Woronoi-Nörlund and Riesz type means in the \(GHM\). Azerb. J. Math. 8(2), 122–141 (2018)

    MathSciNet  MATH  Google Scholar 

  6. Deǧer, U.: A Note on the Degree of Approximation by Matrix Means in the Generalized Hölder Metric. Ukr. Math. J. 68, 545–556 (2016)

    Article  Google Scholar 

  7. Deǧer, U., Küçükaslan, M.: A generalization of deferred Cesàro means and some of their applications, J. Inequal. Appl., 2015:14 ,16 pp (2015)

  8. Deǧer, U., at al.: Approximation by trigonometric polynomials to functions in \(L_{p}\)-norm, Proc. Jangjeon Math. Soc., 15(2), 203–21 (2012)

  9. Gajewski, R., Łenski, W.: On the approximation by the generalized de la Vallée-Poussin means of Fourier series in the spaces \( W^{r}H^{\alpha }\). Math. Nachr. 120, 63–71 (1985)

    Article  MathSciNet  Google Scholar 

  10. Krasniqi, Xh.Z.: On the degree of approximation by Fourier series of functions from the Banach space \(H_{p}^{(\omega )}, p\ge 1\), in generalized Hölder metric. Int. Math. Forum 6(13–16), 613–625 (2011)

    MathSciNet  MATH  Google Scholar 

  11. Leindler, L.: A relaxed estimate of the degree of approximation by Fourier series in generalized Hölder metric. Anal. Math. 35(1), 51–60 (2009)

    Article  MathSciNet  Google Scholar 

  12. Łenski, W., Singh, U., Szal, B.: Trigonometric approximation of functions in seminormed spaces. Math. Inequal. Appl. 24(1), 89–101 (2021)

    MathSciNet  MATH  Google Scholar 

  13. Mohapatra, R.N., Szal, B.: On trigonometric approximation of functions in the \(L^{q}\) norm. Demonstr. Math. 51(1), 17–26 (2018)

    Article  MathSciNet  Google Scholar 

  14. Mohapatra, R.N., Chandra, P.: Degree of approximation of functions in the Hölder metric. Acta Math. Hung. 41(1–2), 67–76 (1983)

    Article  Google Scholar 

  15. Prestin, J., Prössdorf, S.: Error estimates in generalized trigonometric Hölder-Zygmund norms. Z. Anal. Anwendungen 9(4), 343–349 (1990)

    Article  MathSciNet  Google Scholar 

  16. Prössdorf, S.: Zur Konvergenz der Fourierreihen hö lderstetiger Funktionen. (German), Math. Nachr. 69, 7–14 (1975)

    Article  Google Scholar 

  17. Quade, E.S.: Trigonometric approximation in the mean. Duke Math. J. 3, 529–542 (1937)

    Article  MathSciNet  Google Scholar 

  18. Singh, U., Sonker, S.: Degree of approximation of function \( f\in H_{p}^{(w)}\) class in generalized Hölder metric by matrix means, Mathematical modelling and scientific computation, 1-10, Commun. Comput. Inf. Sci., 283, Springer, Heidelberg, (2012)

  19. Singh, M.V., Mittal, M. L.: Approximation of functions in Besov space by deferred Cesàro mean, J. Inequal. Appl., Paper No. 118, 12 pp (2016)

  20. Stypiński, Z.: On a generalization of the theorem of Prö ssdorf. Funct. Approx. Comment. Math. 7, 101–104 (1979)

    MathSciNet  MATH  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Faculty of Education, Department of Mathematics and Informatics, University of Prishtina “Hasan Prishtina”, Avenue “Mother Theresa ”, Prishtinë, 10000, Republic of Kosovo

    Xhevat Z. Krasniqi

  2. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4a, 65-516, Zielona Góra, Poland

    Włodzimierz Łenski & Bogdan Szal

Authors
  1. Xhevat Z. Krasniqi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Włodzimierz Łenski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bogdan Szal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xhevat Z. Krasniqi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krasniqi, X.Z., Łenski, W. & Szal, B. Seminormed approximation by deferred matrix means of integrable functions in \(H_{P}^{(\omega )}\) space. Results Math 77, 145 (2022). https://doi.org/10.1007/s00025-022-01696-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-022-01696-3

Keywords

Mathematics Subject Classification

Search

Navigation