A GENERALIZATION OF THE STRONGLY CESRO
IDEAL CONVERGENCE THROUGH DOUBLE
SEQUENCE SPACES
Carlos Granados
Universidad del Atlntico
Barranquilla, COLOMBIA

Abstract

In this paper, some algebraic properties of Cesáro double ideal convergent sequence spaces are defined and proved. Those spaces are defined as $C_{nm}^{I} $ and $C_{0nm}^{I} $. Furthermore, this paper shows some inclusion relations on these spaces which are established and proved.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 3
Year: 2021

DOI: 10.12732/ijam.v34i3.8

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References

  1. [1] M. Faisal, Some results on strongly Cesaro ideal convergent sequence spaces, Journal of Mathematics, 2020 (2020), 1-4.
  2. [2] G. Hardy and J. Littlewood, Sur la serie de fourier dune fonction a carre sommable, Comptes rendus de l’Academie des Sciences, 156 (1913), 1307- 1309.
  3. [3] V. Khan, H. Fatima, S. Addullah and K. Alshlool, On paranorm BVσ I-convergence double sequence spaces defined by an Orlicz function, Analysis, 37, No 3 (2017), 157-167.
  4. [4] H. Nakano, Concave modulars,Journal of the Mathematical Society of Japan, 5, No 1 (1953), 29-49.
  5. [5] T. Salat, B. C. Tripathy, and M. Ziman, On some properties of I- convergence, Tatra Mountains Mathematical Publications, 28 (2004), 279- 286.
  6. [6] H. Sengul, Some Cesaro-type summability spaces defined by a modulus function of order (α, β), Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 66, No 2 (2017), 80-90.
  7. [7] I. Maddox, Sequence spaces defined by a modulus, Mathematical Proceedings of the Cambridge Philosophical Society, 100, No 1 (1986), 161-166.
  8. [8] M. Et and H. Sengul, Some cesaro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28, No 8 (2014), 1593-1602.
  9. [9] W. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canadian Journal of Mathematics, 25, No 5 (1973), 973-978.
  10. [10] H. Fast, Sur la convergence statistique, Colloquium Mathematicum, 2, No 3-4 (1951), 241-244.
  11. [11] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum, 2, No 1 (1951), 73-74.
  12. [12] J. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313.
  13. [13] J. Fridy, Statistical limit points, Proceedings of the American Mathematical Society, 118, No 4 (1993), 1187.
  14. [14] P. Kostyrko, T.Wilczynski, andW.Wilczynski, I-conver-gence, Real Analysis Exchange, 26, No 2 (2000), 669-686.