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Weihgted Cesaro Sequence Space and Related Matrix Transformation

Received: 4 September 2015     Accepted: 21 September 2015     Published: 13 October 2015
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Abstract

In this paper we define the weighted Cesaro sequence spaces ces (p, q).We prove the space ces (p, q) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual and continuous dual. In section-3 we establish necessary and sufficient condition for a matrix A to map ces (p, q) to l_∞ and ces (p, q) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences. We also get some known and unknown interesting results as corollaries.

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 6)
DOI 10.11648/j.pamj.20150406.12
Page(s) 237-241
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Sequence Space, Kothe-Toeplitz Dual, Matrix Transformation

References
[1] Amit Maji, P. D. Srivastava, On operator ideals using weighted Cesaro sequence space. Journal of the Egyptian Mathematical Society. (2013)1-7
[2] B. Choudhury and S. K. Mishra, On Kothe-Toeplitz duals of certain sequence spaces and their matrix transformations, Indian J. pure appl. Math, 24(15), 291-301, May 1993.
[3] F. M. KHAN and M. F. RAHMAN, Infinite matrices and Cesaro sequence spaces, Analysis Mathematica, 23(1997), 3-11.
[4] G. M. Leibowitz, A note on the Cesaro sequence spaces, Tamkang J. of Math., 2(1971), 151-157.
[5] H. Kizmaz, Canadian Math. Bull. 24(2) (1981), 169-176.
[6] I, J. MADDOX, continuous and Köthe-Toeplitz dual of certain sequence spaces, Proc. Camb. phil. Soc., 65(1969), 431-435.
[7] I, J. MADDOX, Elements of Functional Analysis, Cambridge University Press Cambridge, second edition, 1988.
[8] J, S. Shiue, On the Cesaro sequence spaces, Tamkang J. of Math. 1(1970), 19-25.
[9] K. P. LIM, Matrix transformation in the Cesaro sequence spaces, Kyungpook Math. J. , 14(1974),221-227
[10] K. P. LIM, Matrix transformation on certain sequence space, Tamkang J. of Math. 8(1977), 213-220.
[11] P. D. Johnson Jr. and R. N. Mohapatra, Density of finitely non-zero sequences in some sequence spaces, Math. Japonica 24, No. 3(1979), 253-262.
Cite This Article
  • APA Style

    Md. Fazlur Rahman, A. B. M. Rezaul Karim. (2015). Weihgted Cesaro Sequence Space and Related Matrix Transformation. Pure and Applied Mathematics Journal, 4(6), 237-241. https://doi.org/10.11648/j.pamj.20150406.12

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    ACS Style

    Md. Fazlur Rahman; A. B. M. Rezaul Karim. Weihgted Cesaro Sequence Space and Related Matrix Transformation. Pure Appl. Math. J. 2015, 4(6), 237-241. doi: 10.11648/j.pamj.20150406.12

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    AMA Style

    Md. Fazlur Rahman, A. B. M. Rezaul Karim. Weihgted Cesaro Sequence Space and Related Matrix Transformation. Pure Appl Math J. 2015;4(6):237-241. doi: 10.11648/j.pamj.20150406.12

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  • @article{10.11648/j.pamj.20150406.12,
      author = {Md. Fazlur Rahman and A. B. M. Rezaul Karim},
      title = {Weihgted Cesaro Sequence Space and Related Matrix Transformation},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {6},
      pages = {237-241},
      doi = {10.11648/j.pamj.20150406.12},
      url = {https://doi.org/10.11648/j.pamj.20150406.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150406.12},
      abstract = {In this paper we define the weighted Cesaro sequence spaces ces (p, q).We prove the space ces (p, q) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual and continuous dual. In section-3 we establish necessary and sufficient condition for a matrix A to map ces (p, q) to l_∞ and ces (p, q) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences. We also get some known and unknown interesting results as corollaries.},
     year = {2015}
    }
    

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    AU  - Md. Fazlur Rahman
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    AB  - In this paper we define the weighted Cesaro sequence spaces ces (p, q).We prove the space ces (p, q) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual and continuous dual. In section-3 we establish necessary and sufficient condition for a matrix A to map ces (p, q) to l_∞ and ces (p, q) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences. We also get some known and unknown interesting results as corollaries.
    VL  - 4
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Author Information
  • Department of Mathematics, Eden University College, Dhaka, Bangladesh

  • Department of Mathematics, Eden University College, Dhaka, Bangladesh

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