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On Certain Paranormed Difference Sequence Spaces Derived from Generalized Weighted Mean


Affiliations
1 Department of Mathematics, KIIT University, Bhbaneswar 751 024, India
2 Department of Mathematics, Utkal University, Bhubaneswar 751 004, India
     

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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.
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  • On Certain Paranormed Difference Sequence Spaces Derived from Generalized Weighted Mean

Abstract Views: 234  |  PDF Views: 2

Authors

P. Baliarsingh
Department of Mathematics, KIIT University, Bhbaneswar 751 024, India
S. Dutta
Department of Mathematics, Utkal University, Bhubaneswar 751 004, India

Abstract


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