Neyaz Ahmad Sheik, Ab. Hamid Ganie, "A New Type of Sequence Space of Non-Absolute Type and Matrix Transformation," WSEAS Transactions on Mathematics, vol. 12, pp. -, 2013, DOI:
Neyaz Ahmad Sheik, Ab. Hamid Ganie. A New Type of Sequence Space of Non-Absolute Type and Matrix Transformation.
WSEAS Transactions on Mathematics. 2013;12:-.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
A New Type of Sequence Space of Non-Absolute Type and Matrix Transformation
Authors: ,
Abstract: In this paper, we introduce the space $$r^q ( Δ_{u}^{p})$$, where $$r^q ( Δ_{u}^{p}) = \lbrace x =(x_{k}) ∈ ω : (△x_{k} ) ∈ r^q (u, p)
\rbrace$$; where $$ r^q (u, p)$$ has recently been introduced and studied by Neyaz and Hamid (Acta Math. Acad. Paeda. Nyreg., 28, 2012, pp. 47-58). We show its completeness property, prove that the space $$r^q ( Δ_{u}^{p})$$ and $$l(p)$$ are linearly isomorphic and compute $$α -, β- $$ and $$γ-$$duals of $$r^q ( Δ_{u}^{p})$$. Moreover, we construct the basis of $$r^q ( Δ_{u}^{p})$$. Finally, we characterize some matrix class.
Keywords:
Sequence space of non-absolute type, paranormed sequence space, α-, β- and γ-duals, matrix transformations
Pages: - WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 12, 2013DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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