Weihgted Cesaro Sequence Space and Related Matrix Transformation

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

doi:doi:10.11648/j.pamj.20150406.12

| Peer-Reviewed

Weihgted Cesaro Sequence Space and Related Matrix Transformation

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

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 6)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Weihgted Cesaro Sequence Space and Related Matrix Transformation
AU  - Md. Fazlur Rahman
AU  - A. B. M. Rezaul Karim
Y1  - 2015/10/13
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150406.12
DO  - 10.11648/j.pamj.20150406.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 237
EP  - 241
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150406.12
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
IS  - 6
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). 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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Weihgted Cesaro Sequence Space and Related Matrix Transformation
AU  - Md. Fazlur Rahman
AU  - A. B. M. Rezaul Karim
Y1  - 2015/10/13
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150406.12
DO  - 10.11648/j.pamj.20150406.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 237
EP  - 241
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150406.12
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
IS  - 6
ER  -

Copy | Download