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

  • BATAINEH AHMAD H. A. (Department of Mathematics Al al-Bayt University) ;
  • AL-ZA'AREER HAMZA B. (Department of Mathematics Al al-Bayt University)
  • Published : 2005.10.01

Abstract

Let F be a non-trivial non-Archimedian field. The sequence spaces $\Gamma\;(F)\;and\;{\Gamma}^{\ast}(F)$ 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 $U\;=\;(U_k),\;U_k\;{\neq}\;0 \;(\;k\;=\;1,2,3,{\cdots})$. 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 $\Gamma(u,\;F,\;{\Delta}),\;{\Gamma}^{\ast}(u,\;F,\;{\Delta}),\;l_p(u,\;F,\;{\Delta})$), and $b_v(u,\;F,\;{\Delta}$). We also study some matrix transformations on these new spaces.

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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