Skip to main content
SpringerLink
Log in

Inclusion results on statistical cluster points

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

We study the concepts of statistical cluster points and statistical core of a sequence for A λ methods defined by deleting some rows from a nonnegative regular matrix A. We also relate A λ-statistical convergence to A μ-statistical convergence. Finally we give a consistency theorem for A-statistical convergence and deduce a core equality result.

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. D. H. Armitage and I. J. Maddox, A new type of Cesàro mean, Analysis, 9 (1989), 195–204.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Connor, Two valued measures and summability, Analysis, 10 (1990), 373–385.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Connor and J. Kline, On statistical limit points and the consistency of statistical convergence, J. Math. Anal. App., 197 (1996), 392–399.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. Demirci, A-statistical core of a sequence, Demonstratio Math., 33 (2000), 343–353.

    MathSciNet  MATH  Google Scholar 

  5. K. Demirci, On A-statistical cluster points, Glas. Mat., 37(57) (2002), 293–301.

    MathSciNet  MATH  Google Scholar 

  6. A. R. Freedman and J. J. Sember, Densities and summability, Pacific J. Math., 95 (1981), 293–305.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc., 118 (1993), 1187–1192.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. A. Fridy and M. K. Khan, Tauberian theorems via statistical convergence, J. Math. Anal. Appl., 228 (1998), 73–95.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., 125 (1997), 3625–3631.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. A. Fridy and C. Orhan, Statistical core theorems, J. Math. Anal. Appl., 228 (1997), 520–527.

    Article  MathSciNet  MATH  Google Scholar 

  11. C. Goffman and G. M. Petersen, Submethods of regular matrix summability methods, Canad. J. Math., 8 (1956), 40–46.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. K. Khan and C. Orhan, Matrix characterization of A-statistical convergence, J. Math. Anal. Appl., 335 (2007), 406–417.

    Article  MathSciNet  MATH  Google Scholar 

  13. E. Kolk, Matrix summability of statistical convergent sequences, Analysis, 13 (1993), 77–83.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Li and J. A. Fridy, Matrix transformations of statistical cores of complex sequences, Analysis, 20 (2000), 15–34.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (1995), 1811–1819.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Osikiewicz and M. K. Khan, Inclusion results for convolution submethods, Int. J. Math. Math. Sci., 2004, 55–64.

    Google Scholar 

  17. G. M. Petersen, Summability methods and bounded sequences, J. London Math. Soc., 31 (1956), 324–326.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences, International University of Sarajevo, 71000, Sarajevo, Bosnia-Herzegovina

    H. I. Miller & L. Miller-Wan Wieren

  2. Department of Mathematics, Ahi Evran University, Faculty of Science and Arts, Kirşehir, Turkey

    E. Taş

  3. Faculty of Science and Arts, Department of Mathematics, Hitit University, Ulukavak, Çorum, 19030, Turkey

    T. Yurdakadim

Authors
  1. H. I. Miller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Miller-Wan Wieren
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Taş
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. Yurdakadim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Yurdakadim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Miller, H.I., Wieren, L.MW., Taş, E. et al. Inclusion results on statistical cluster points. Anal Math 42, 165–172 (2016). https://doi.org/10.1007/s10476-016-0205-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10476-016-0205-y

Key words and phrases

Mathematics Subject Classification

Search

Navigation