Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON A GENERALIZED DIFFERENCE SEQUENCE SPACES DEFINED BY A MODULUS FUNCTION AND STATISTICAL CONVERGENCE

  • Bataineh Ahmad H.A. (Department of Mathematics Al al-Bayt University)
  • Published : 2006.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

Keywords

References

  1. T. Bilgen, On statistical convergence, An. Univ. Timisoara Ser. Math. Inform. 32 (1994), no. 1, 3-7
  2. J. S. Connor, The statistical and strong p-Oesaro convergence of sequences, Analysis 8 (1988), 47-63
  3. H. Fast, Sur la convergence statistique, Collaq. Math. 2 (1951), 241-244 https://doi.org/10.4064/cm-2-3-4-241-244
  4. M. Et and M. Basarir, On some new generalized difference sequence spaces, Periodica Mathematica Hungaria 35 (1997), no. 3, 169-175 https://doi.org/10.1023/A:1004597132128
  5. M. Et and C. A. Bektas, Generalized strongly (V, ${\lambda}$)-summable difference sequences defined by Orlicz functions, (under communication)
  6. M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. of Math. 21 (1995), 377-386
  7. M. Et., Y. Altin and H. Altinok, On some generalized difference sequence spaces defined by a modulus junctions, Filomat 17 (2003), 23-33
  8. J. A. Friday, On statistical convergence, Analysis, 5 (1985), 301-313
  9. P. Kampthan and M. Gupta, Sequence Spaces and Series, Marcel Dekkar Inc., New York, 1980
  10. H. Kizmaz, On certain sequence spaces, Cnad. Math. Bull. 24 (1981), 169-176 https://doi.org/10.4153/CMB-1981-027-5
  11. E. Kolak, The statistical convergence in sequence spaces, Acta. Comment. Univ. Tartu 928 (1991), 41-52
  12. L. Leindler, Uber die la Vallee-Pousinsche Summierbarkeit Allgemeiner Orthogonal-reihen, Acta Math. Acad. Sci. Hungar 16 (1965), 375-387 https://doi.org/10.1007/BF01904844
  13. Mursallen, ${\lambda}$-statistical convergence, Math. Slovaca 50 (2000), 111-115
  14. I. J. Maddox, Elements of Functional Analysis, Cambridge Univ. Press, 1970
  15. I. J. Maddox, Sequence spaces defined by a modulus, Mat. Proc. Camb. Phil. Soc. 100 (1986), 161-166
  16. E. Malkowsky and S. D. Parashar, Matrix transformations in sequences of bounded and convergent difference sequences of order m, Analysis 17 (1997), 87-97 https://doi.org/10.2307/3326695
  17. E. Malkowsky and E. Savas, Some ${\lambda}$-sequence spaces defined by a modulus, Archivum Mathematicum 36 (2000), 219-228
  18. W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973-978 https://doi.org/10.4153/CJM-1973-102-9
  19. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139-150
  20. E. Savas, On some generalized sequence spaces defined by a modulus, Indian J. pure and appl. Math. 30 (1999), no. 5, 459-464
  21. A. Wilansky, Summabilitry Through Functional Analysis, North-Holland Mathematics Studies, (85), North-Holland, 1984