DOI QR코드

DOI QR Code

ON DEFERRED CESÀRO MEAN IN PARANORMED SPACES

  • Ercan, Sinan (Department of Mathematics, Firat University)
  • Received : 2020.11.12
  • Accepted : 2021.02.16
  • Published : 2021.03.30

Abstract

The aim of the present study is to introduce the concepts of deferred statistical convergence, deferred statistical Cauchy sequence and deferred Cesàro summability in paranormed spaces. We investigate some properties of these concepts and some inclusion relations with examples.

Keywords

References

  1. R. P. Agnew, On deferred Cesaro Mean, Comm. Ann. Math. 33 (1932), 413-421. https://doi.org/10.2307/1968524
  2. A. Alotaibi, A. M. Alroqi, Statistical convergence in a paranormed space, J. Inequal. Appl. 2012, 2012:39, 6 pp.
  3. M. Altinok, B. Inan, M. Kucukaslan, On deferred statistical convergence of sequences of sets in metric space, TJMCS, Article ID 20150050, (2015), 9 pages.
  4. M. Candan, A. Gunes, Paranormed sequence space of non-absolute type founded using generalized difference matrix, Proc. Nat. Acad. Sci. India Sect. A, 85 2 (2015), 269-276. https://doi.org/10.1007/s40010-015-0204-6
  5. M. Candan, A new perspective on paranormed Riesz sequence space of non-absolute type, Glob. J. Math. Anal., 3 4 (2015), 150-163. https://doi.org/10.14419/gjma.v3i4.5573
  6. J. S. Connor, The statistical and strong p-Cesaro of sequences, Analysis, 8 (1988), 47-63. https://doi.org/10.1524/anly.1988.8.12.47
  7. S. Ercan, Y. Altin, M. Et, V. K. Bhardwaj, On deferred weak statistical convergence, J. Anal., (2020), https://doi.org/10.1007/s41478-020-00221-5.
  8. H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  9. J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313. https://doi.org/10.1524/anly.1985.5.4.301
  10. M. Ilkhan, E. E. Kara, A new type of statistical Cauchy sequence and its relation to Bourbaki completeness, Cogent Math. Stat., 5:1, 1487500 (2018), 9 pages. https://doi.org/10.1080/25742558.2018.1487500
  11. M. Ilkhan, E. E. Kara, On statistical convergence in quasi-metric spaces, Demonstr. Math. 52 (1) (2019), 225-236. https://doi.org/10.1515/dema-2019-0019
  12. C. Kosar, M. Kucukaslan, M. Et, On asymptotically deferred statistical equivalence of sequences, Filomat, 31:16 (2017), 5139-5150. https://doi.org/10.2298/FIL1716139K
  13. M. Kucukaslan, M. Yilmazturk, On deferred statistical convergence of sequences, Kyungpook Math. J., no. 2, 56 (2016), 357-366. https://doi.org/10.5666/KMJ.2016.56.2.357
  14. I. J. Maddox, Elements of Functional Analysis, Cambridge at the University Press, (1970).
  15. A. Mohammed, M. Mursaleen, λ-statistical convergence in paranormed space, Abstr. Appl. Anal. 2013, Art. ID 264520, 5 pp.
  16. H. Roopaei, T. Yaying, Quasi-Cesaro matrix and associated sequence space, Turkish J. Math. 45 (1) (2021), 153-166. https://doi.org/10.3906/mat-2009-54
  17. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139-150.
  18. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74. https://doi.org/10.4064/cm-2-2-98-108
  19. F. Temizsu, M. Et, M. Cinar, ∆m-deferred statistical convergence of order α, Filomat 30 3 (2016), 667-673. https://doi.org/10.2298/FIL1603667T
  20. N. Turan, E. E. Kara, M. Ilkhan, Quasi statistical convergence in cone metric spaces, Facta Univ. Ser. Math. Inform. 33 (4) (2018), 613-626.
  21. T. Yaying, B. Hazarika, Lacunary arithmetic statistical convergence, Natl. Acad. Sci. Lett., 43 (2020), 547-551. https://doi.org/10.1007/s40009-020-00910-6
  22. T. Yaying, B. Hazarika, M. Mursaleen, On sequence space defined by the domain of q-Cesaro matrix in ℓp space and the associated operator ideal, J. Math. Anal. Appl. 493 (1) (2021), 124453. https://doi.org/10.1016/j.jmaa.2020.124453
  23. T. Yaying, Paranormed Riesz difference sequence spaces of fractional order, Kragujevac J. Math. 46 (2) (2022), 175-191.
  24. T. Yaying, B. Hazarika, A. Esi, Geometric properties and compact operators on fractional Riesz difference spaces, Kragujevac J. Math. 47 (4) (2023), 545-566.
  25. M. Yilmazturk, M. Kucukaslan, On strongly defereed Cesaro summability and deferred statistical convergence of the sequences, Bitlis Eren Univ. J. Sci. Technology 3 (2011), 22-25. https://doi.org/10.17678/beuscitech.47136
  26. A. Zygmund, Trigonometrical Series, Monogr. Mat. 5. Warszawa-Lwow 1935.