ON A GENERALIZED DIFFERENCE SEQUENCE SPACES OVER NON-ARCHIMEDIAN FIELDS AND RELATED MATRIX TRANSFORMATIONS

- Journal title : Communications of the Korean Mathematical Society
- Volume 20, Issue 4, 2005, pp.723-729
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2005.20.4.723

Title & Authors

ON A GENERALIZED DIFFERENCE SEQUENCE SPACES OVER NON-ARCHIMEDIAN FIELDS AND RELATED MATRIX TRANSFORMATIONS

BATAINEH AHMAD H. A.; AL-ZA'AREER HAMZA B.;

BATAINEH AHMAD H. A.; AL-ZA'AREER HAMZA B.;

Abstract

Let F be a non-trivial non-Archimedian field. The sequence spaces were defined and studied by Soma-sundaram[4], where these spaces denote the spaces of entire and analytic sequences defined over F, respectively. In 1997, these spaces were generalized by Mursaleen and Qamaruddin[1] by considering an arbitrary sequence . They characterized some classes of infinite matrices considering these new classes of sequences. In this paper, we further generalize the above mentioned spaces and define the spaces ), and ). We also study some matrix transformations on these new spaces.

Keywords

difference sequence spaces;non-Archimedian field;matrix transformations;

Language

English

References

1.

M. Mursaleen and Qamaruddin, Some new sequence spaces over non-Archimedian fields and their matrix transformations, Bull. Calcutta Math. Soc. 89 (1997), 81-86

2.

S. Nanda, Some topological vector spaces over valued fields, Bull. Inst. Math. Acad. Sinica 9 (1981), no. 4, 461-467

3.

S. M. Sirajudeen and A. Sulaiman, Inclusion theorems of some sequence spaces over non-Archimedian fields, Indian J. Pure Appl. Math. 26 (1995), no. 5, 445-449

4.

D. Somasundaram, Inclusion theorems on matrix transformation of some sequence spaces over non-Archimedian fields, Boll. Unione Mat. Ital. 6 (1970), 935-960

5.

D. Somasundaram, Inclusion theorems on matrix transformation of some sequence spaces over non-Archimedian fields II, Indian J. Pure Appl. Math. 5 (1974), 327-332