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.