Some new type of difference sequence space of nonabsolute type and some matrix transformation

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Some new type of difference sequence space of nonabsolute type and some matrix transformation

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ABSTRACT

In this paper, we introduce the space r q (p u ), where r q (p u ) = {x = (xk) ∈ ω : (ukxj ) ∈ r q (u, p) < ∞} ; where r q (u, p) has recently been studied by Neyaz and Hamid. We show its completeness property, prove that the space r q (p u ) and l(p) are linearly isomorphic and compute their α -, β- and γ-duals. Furthermore construct the basis of r q (u, p). In our last section we characterize some matrix class.

KEYWORDS

Sequence space of non-absolute type; paranormed sequence space; α-, β- and γ-duals ; matrix transformations.

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Cite this paper

Ab. Hamid Ganie. (2016) Some new type of difference sequence space of nonabsolute type and some matrix transformation. International Journal of Mathematical and Computational Methods, 1, 48-57