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Baliarsingh, P.
- On the Class of New Difference Sequence Spaces
Abstract Views :207 |
PDF Views:1
Authors
P. Baliarsingh
1,
S. Dutta
2
Affiliations
1 Department of Mathematics, Trident Academy of Technology, Infocity, Bhubaneswar -751024, IN
2 Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, IN
1 Department of Mathematics, Trident Academy of Technology, Infocity, Bhubaneswar -751024, IN
2 Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, IN
Source
The Journal of the Indian Mathematical Society, Vol 80, No 3-4 (2013), Pagination: 203-211Abstract
The main purpose of the present paper is to introduce a new class of difference sequence spaces l∞(Δ[k], ν,p),c0(Δ[k], ν,p) and c(Δ[k], ν,p), where Δ[k](xk) = kxk - (k+1)xk+1 for all k = 1,2,3.... Also, we derive some inclusion relations and other topological properties of these spaces. Finally we discuss about their α-, β-, and γ- duals.Keywords
Difference Sequence Spaces α-, β-, and γ- Duals.
- On Certain Paranormed Difference Sequence Spaces Derived from Generalized Weighted Mean
Abstract Views :234 |
PDF Views:2
Authors
P. Baliarsingh
1,
S. Dutta
2
Affiliations
1 Department of Mathematics, KIIT University, Bhbaneswar 751 024, IN
2 Department of Mathematics, Utkal University, Bhubaneswar 751 004, IN
1 Department of Mathematics, KIIT University, Bhbaneswar 751 024, IN
2 Department of Mathematics, Utkal University, Bhubaneswar 751 004, IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 1-2 (2016), Pagination: 13-25Abstract
The main objective of the present article is to give a unifying approach to most of the paranormed difference sequence spaces defined in the domain of weighted mean operator. In this work, we introduce certain new paranormed spaces such as l∞(μ, ν; Δr, p), c0(μ, ν; Δr, p), c(μ, ν; Δr, p) and l(μ, ν; Δr, p) by combining the generalized difference operator Δr and the weighted mean operator G(μ, ν). Also we investigate their topological structures and establish their α-, β- and γ- duals. Moreover we characterize the matrix transformations from these spaces to the basic sequence spaces l∞(q), co(q), c(q) and l(q).Keywords
Difference Operator Δr, Generalized Weighted Mean Operator G(μ, ν), Paranormed Difference Sequence Spaces, α, β and γ Duals, Matrix Transformations.References
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- P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput., 219(18) (2013), 9737–9742.
- P. Baliarsingh and S. Dutta, On certain new difference sequence spaces generated by infinite matrices, Thai. J. Math., 11(1) (2013), 75–86.
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- S. Dutta and P. Baliarsingh, On the fine spectra of the generalized rth difference operator Δrν on the sequence space ℓ1, Appl. Math. Comput., 219(4) (2012), 1776–1784.
- S. Dutta, P. Baliarsingh, On the spectrum of 2-nd order generalized difference operator Δ2 over the sequence space co, Bol. Soc. Paran. Mat., 31(2) (2013), 235–244.
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- On Double Difference Operators via Four Dimensional Matrices
Abstract Views :339 |
PDF Views:13
Authors
Affiliations
1 Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar-751024, IN
1 Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar-751024, IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 3-4 (2016), Pagination: 209-219Abstract
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.Keywords
Difference Operators 2Δr, 2Δ(r), Four Dimensional Matrix Transformations.References
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- 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.
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