On Double Difference Operators via Four Dimensional Matrices

Jump To References Section

Authors

  • P. Baliarsingh
     Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar-751024 ,IN

Keywords:

Difference Operators 2Δ, r, 2Δ, (r), Four Dimensional Matrix Transformations.

Abstract

In the present article, we define the double difference operators 2Δr and 2Δ(r) of integral order r. Using matrix transformations, these two difference operators are being expressed by 4-dimensional infinite matrices. We find their inverse operators through four dimensional matrix characterizations. Also, certain relations are being established among these operators with their inverses.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2016-12-01

How to Cite

Baliarsingh, P. (2016). On Double Difference Operators via Four Dimensional Matrices. The Journal of the Indian Mathematical Society, 83(3-4), 209–219. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/6604

Issue

Volume 83, Issue 3-4, July-December 2016

Section

Articles

License

Copyright (c) 2016 P. Baliarsingh

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

B. Altay, F. Ba¸sar, Some new spaces of double sequences, J. Math. Anal. Appl., 309(1) (2005), 70-90.

P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput. 219(18) (2013), 9737-9742.

P. Baliarsingh, S. Dutta, On the classes of fractional order difference sequence spaces and their matrix transformations, Appl. Math. Comput., 250 (2015), 665-674.

P. Baliarsingh, A note on paranormed difference sequence spaces of fractional order and their matrix transformations, J. Egypt. Math. Soc., 22(2) (2014), 249-253.

M. Et, R. Colak, On some generalized difference sequence spaces, Soochow J. Math., 21(4) (1995), 377-386.

H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24(2) (1981), 169-176.

A. Pringsheim, Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann., 53 (1900), 289-321.

R. F. Patterson, Double sequence core theorem, Int. J. Math. Math. Sci., 22 (1999), 785-793.

G. M. Robinson, Divergent double sequences and series, Trans. Amer. Math. Soc., 28 (1926), 50-73.

E. Savas, R.F. Patterson, Double sequence spaces defined by a modulus, Math. Slovaca, 61 (2011), 245-256.

E. Savas, On strong double matrix summability via ideals, Filomat, 26(6) (2012), 1143-1150.

U. Ulusu, F. Nuray, On strongly lacunary summability of sequences of sets, J. Appl. Math. Bioinform. 3(3) (2013), 75-88.

M. Zeltser, M. Mursaleen, S.A. Mohiuddine, On almost conservative matrix methods for double sequence spaces, Publ. Math. Debrecen., 75 (2009), 1-13.