On a new difference sequence space

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-03-0035

Keywords:

Difference operators, Cesàro operator C(1, 1), Abel transformation, Eigenvalues

Abstract

In the present note, we define a new difference sequence Dx =(Dx)n with the help of difference operator D as

 

Also, we discuss some interesting properties of the proposed difference operator D.

Downloads

Download data is not yet available.

Author Biographies

  • P. Baliarsingh, Gangadhar Meher University.

    Dept. of Mathematics.

  • L. Nayak, Kalinga Institute of Industrial Technology.

    Dept. of Mathematics, School of Applied Sciences.

  • P. Beuria, Kalinga Institute of Industrial Technology.

    Dept. of Mathematics, School of Applied Sciences.

References

Z. U. Ahmad, M. Mursaleen, “Köthe-Toeplitz duals of some new sequence spaces and their matrix maps”, Publications de L’Institut Mathématique, vol. 42, no. 56, pp. 57-61, 1987. [On line]. Available: https://bit.ly/2AXioWz

B. Altay and F. Başar, “On the fine spectrum of the difference operator Δ on c0 and c”, Information sciences, vol. 168, no. 1-4, pp. 217–224, Dec. 2004, doi: 10.1016/j.ins.2004.02.007

P. Baliarsingh, “Some new difference sequence spaces of fractional order and their dual spaces”, Applied mathematics and computation, vol. 219, no. 18, pp. 9737–9742, May 2013, doi: 10.1016/j.amc.2013.03.073

P. Baliarsingh and S. Dutta, “A unifying approach to the difference operators and their applications”, Boletim da Sociedade Paranaense de Matemática, vol. 33, no. 1, p. 49, 2013., doi: 10.5269/bspm.v33i1.19884

P. Baliarsingh and S. Dutta, “On the classes of fractional order difference sequence spaces and their matrix transformations”, Applied mathematics and computation, vol. 250, pp. 665–674, Jan. 2015, doi: 10.1016/j.amc.2014.10.121

P. Baliarsingh, “On a fractional difference operator”, Alexandria engineering journal, vol. 55, no. 2, pp. 1811–1816, Jun. 2016, doi: 10.1016/j.aej.2016.03.037

P. Baliarsingh and S. Dutta, “On certain Toeplitz matrices via difference operator and their applications”, Afrika matematika, vol. 27, no. 5-6, pp. 781–793, Aug. 2015, doi:10.1007/s13370-015-0374-z

B. Choudhary, S.K. Mishra, “On Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations”, Indian journal of pure and applied mathematics, vol. 24, no. 5, pp. 291301, 1993. [On line]. Available: https://bit.ly/3bVmNWz

M. Et and R. Çolak, “On some generalized difference sequence spaces”, Soochow journal of mathematics, vol. 21, no. 4, pp. 377-386, Oct. 1995. [On line]. Available: https://bit.ly/2AWvT8V

H. Bilgiç and H. Furkan, “On the fine spectrum of the generalized difference operator B (r,s) over the sequence spaces ℓp and bvp, (1 < p < ∞), “Nonlinear analysis: theory, methods & applications”, vol. 68, no. 3, pp. 499–506, Feb. 2008, doi: 10.1016/j.na.2006.11.015

H. Kizmaz, “On certain sequence spaces”, Canadian mathematical bulletin, vol. 24, no. 2, pp. 169–176, Jun. 1981, doi: 10.4153/CMB-1981-027-5

P-N. Ng and P-Y. Lee, “Cesàro sequence spaces of non-absolute type”, Commentationes mathematicae, vol. 20, no. 2, pp. 429-433, 1978. [On line]. Available: https://bit.ly/2ZvWi7z

Downloads

Published

2020-06-03

Issue

Section

Artículos

How to Cite

[1]
“On a new difference sequence space”, Proyecciones (Antofagasta, On line), vol. 39, no. 3, pp. 581–589, Jun. 2020, doi: 10.22199/issn.0717-6279-2020-03-0035.

Most read articles by the same author(s)