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

Md. Fazlur Rahman; A. B. M. Rezaul Karim

doi:doi:10.11648/j.pamj.20150403.15

| Peer-Reviewed

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

Md. Fazlur Rahman, A. B. M. Rezaul Karim

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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
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 Mappin

References

[1]	C. G. Lascarides and I. J. Maddox, Matrix transformations between some classes of sequences, Proc. Cambridge Philos. Soc., 68(1970), 99-104.
[2]	E. Bulut and O. Cakar, The sequence space and related matrix transformations, communication de la faculatedes sciences d L’universite D’Ankara Tome, 28(1979), 33-44.
[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.
[4]	G.M. Petersen, Regular matrix transformations, Mc Graw-Hill publishing Co. Ltd., London-New York-Toronto, Ont., 1966.
[5]	H. Nakano, Modulared sequence spaces, Proc. Japan Acad., 27(1951), 508-512.
[6]	I. J. Maddox, Elements of functional analysis, Cambridge University Press, Cambridge, second edition, 1988.
[7]	I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford Ser., (2),18 (1967), 345-355.
[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.
[16]	N. A. Sheikh and A B H Ganie, “A new paranormed sequence space and some matrix transformations”, Acta Math. Acad. Paedagogicae Nyiregyhaiensis, 28(2012),47-58.
[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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping
AU  - Md. Fazlur Rahman
AU  - A. B. M. Rezaul Karim
Y1  - 2015/05/15
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.15
DO  - 10.11648/j.pamj.20150403.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 90
EP  - 95
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.15
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  -

Copy | Download

Author Information

Md. Fazlur Rahman

Department of Mathematics, Eden University College, Dhaka, Bangladesh
A. B. M. Rezaul Karim

Department of Mathematics, Eden University College, Dhaka, Bangladesh

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Generalized Riesz Sequence Space of Non-Absolute Type and Some Matrix Mapping
AU  - Md. Fazlur Rahman
AU  - A. B. M. Rezaul Karim
Y1  - 2015/05/15
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.15
DO  - 10.11648/j.pamj.20150403.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 90
EP  - 95
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.15
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  -

Copy | Download