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Volume 33, Issue 4
On a Difference Matrix and Its Properties

P. Baliarsingh & L. Nayak

DOI: 10.4208/ata.2017.v33.n4.7

Anal. Theory Appl., 33 (2017), pp. 375-383.

Published online: 2017-11

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  • Abstract

In the present paper, a new difference matrix via difference operator $D$ is introduced. Let $x = (x_k)$ be a sequence of real numbers, then the difference operator $D$ is defined by $D(x)_n = ∑^n_{k=0} (−1)^k\Bigg(\begin{matrix}n \\ n−k \end{matrix}\Bigg)x_k$, where $n = 0,1,2,3,···$. Several interesting properties of the new operator $D$ are discussed.

  • Keywords

Difference operators $∆^α$, $B(r,s)$, $B(r,s,t,u)$, $D$, Cesàro operator $C(1,1)$.

  • AMS Subject Headings

46A45, 46A35, 46B45

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-33-375, author = {P. Baliarsingh and L. Nayak}, title = {On a Difference Matrix and Its Properties}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {4}, pages = {375--383}, abstract = {

In the present paper, a new difference matrix via difference operator $D$ is introduced. Let $x = (x_k)$ be a sequence of real numbers, then the difference operator $D$ is defined by $D(x)_n = ∑^n_{k=0} (−1)^k\Bigg(\begin{matrix}n \\ n−k \end{matrix}\Bigg)x_k$, where $n = 0,1,2,3,···$. Several interesting properties of the new operator $D$ are discussed.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n4.7}, url = {http://global-sci.org/intro/article_detail/ata/10704.html} }
TY - JOUR T1 - On a Difference Matrix and Its Properties AU - P. Baliarsingh & L. Nayak JO - Analysis in Theory and Applications VL - 4 SP - 375 EP - 383 PY - 2017 DA - 2017/11 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n4.7 UR - https://global-sci.org/intro/article_detail/ata/10704.html KW - Difference operators $∆^α$, $B(r,s)$, $B(r,s,t,u)$, $D$, Cesàro operator $C(1,1)$. AB -

In the present paper, a new difference matrix via difference operator $D$ is introduced. Let $x = (x_k)$ be a sequence of real numbers, then the difference operator $D$ is defined by $D(x)_n = ∑^n_{k=0} (−1)^k\Bigg(\begin{matrix}n \\ n−k \end{matrix}\Bigg)x_k$, where $n = 0,1,2,3,···$. Several interesting properties of the new operator $D$ are discussed.

P. Baliarsingh and L. Nayak. (2017). On a Difference Matrix and Its Properties. Analysis in Theory and Applications. 33 (4). 375-383. doi:10.4208/ata.2017.v33.n4.7
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