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Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping

Received: 20 April 2015     Accepted: 4 May 2015     Published: 15 May 2015
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Abstract

Recently several authors defined and studied Riesz sequence space r^q(u, p) of non-absolute type. In this paper for some weight s ≥ 0, we define the generalized Risez sequence space r^q(u, p, s) of non-absolute type and determine its Kothe-Toeplitz dual. We also consider the matrix mapping r^q(u, p, s) to l_∞ and r^q(u, p, s) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences.

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3)
DOI 10.11648/j.pamj.20150403.15
Page(s) 90-95
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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 Mappin

References
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[3] F.M. Khan and M.A. Khan, The sequence space ces(p, s) and related matrix transformations, Research Ser.Mat., 21(1991); 95-104.
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[8] I.J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Cambridge Philo. Soc., 64(1968), 335-340.
[9] I. J. Maddox, Continuous and Kothe-Toeplitz dual of certain sequence spaces, Proc.Camb.Phil.Soc., 65(1969), 431-435.
[10] K. G. Grosse-Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math.,Aual.appl., 180(1)(1993), 223-238.
[11] L. N. Mishra, V. N. Mishra and V. Sonavane, Trigonometric approximation of functions belonging to Lipschitz class by matrix operator of conjugate series of Fourier series, Advances in Difference Equations, a Springer Journal,(2013),2013:127.
[12] L. N. Mishra, V. N. Mishra, K. Khatri, Deepmala, On The Trigonometric approximation of signals belonging to generalized weighted Lipschitz class by matrix operator of conjugate series of its Fourier series, Applied Mathematics and Computation,(Elsevier Journal), Vol.237 (2014) 252-263.
[13] Mursaleen, Matrix transformations between the new sequence spaces, Houston J. Math., 9(4)(1993),505-509.
[14] M. L. Mittal, V.N. Mishra, Approximation of signals (functions) belonging to the weighted class by almost matrix summability method of its Fourier series, International J. of Math. Sci. & Engg. Appls. (IJMSEA) Vol. 2 No.IV (2008), 285-294.
[15] M. Stieglitz and Tietz, Math. Z., 154(1977),1-16.
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[17] V.N. Mishra, K. Khatri, L.N. Mishra and Deepmala, Trigonometric approximation of periodic signals belonging to generalized weighted Lipschitz class by Norlund-Euler operator of conjugate series of its Fourier series. Journal of Classical analysis, Vol-5, 2(2014), 91-105.
[18] V.N. Mishra, H.H. Khan, I.A. Khan, L.N. Mishra, On the degree of approximation of signals of Lipschitz class by almost Riesz mans of its Fourier series, Journal of Classical analysis, Vol-4, Number 1(2014), 79-87.
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  • APA Style

    Md. Fazlur Rahman, A. B. M. Rezaul Karim. (2015). Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping. Pure and Applied Mathematics Journal, 4(3), 90-95. https://doi.org/10.11648/j.pamj.20150403.15

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    ACS Style

    Md. Fazlur Rahman; A. B. M. Rezaul Karim. Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping. Pure Appl. Math. J. 2015, 4(3), 90-95. doi: 10.11648/j.pamj.20150403.15

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    AMA Style

    Md. Fazlur Rahman, A. B. M. Rezaul Karim. Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping. Pure Appl Math J. 2015;4(3):90-95. doi: 10.11648/j.pamj.20150403.15

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  • @article{10.11648/j.pamj.20150403.15,
      author = {Md. Fazlur Rahman and A. B. M. Rezaul Karim},
      title = {Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {3},
      pages = {90-95},
      doi = {10.11648/j.pamj.20150403.15},
      url = {https://doi.org/10.11648/j.pamj.20150403.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.15},
      abstract = {Recently several authors defined and studied Riesz sequence space r^q(u, p) of non-absolute type. In this paper for some weight s ≥ 0, we define the generalized Risez sequence space r^q(u, p, s) of non-absolute type  and determine its Kothe-Toeplitz dual. We also consider the matrix mapping r^q(u, p, s) to l_∞ and r^q(u, p, s) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences.},
     year = {2015}
    }
    

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    T1  - Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping
    AU  - Md. Fazlur Rahman
    AU  - A. B. M. Rezaul Karim
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    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
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    AB  - Recently several authors defined and studied Riesz sequence space r^q(u, p) of non-absolute type. In this paper for some weight s ≥ 0, we define the generalized Risez sequence space r^q(u, p, s) of non-absolute type  and determine its Kothe-Toeplitz dual. We also consider the matrix mapping r^q(u, p, s) to l_∞ and r^q(u, p, s) to c, where l_∞ is the space of all bounded sequences and c is the space of all convergent sequences.
    VL  - 4
    IS  - 3
    ER  - 

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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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