Filomat 2010 Volume 24, Issue 3, Pages: 103-109
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Matrix transformations of strongly convergent sequences into Vσ

Mohiuddine S.A., Aiyub M.

In this paper, we define the spaces ω(p, s) and ωp (s), where ω(p, s) = {x:1/nΣ k=1 K-s |xk -ℓ|pk → 0 for some ℓ, s ≥ 0} and if pk = p for each k, we have ω(p, s)=ωp(s). We further characterize the matrix classes (ω(p, s), Vσ ), (ωp (s), Vσ ) and (ωp (s), Vσ )reg , where Vσ denotes the set of bounded sequences all of whose σ-mean are equal.

Keywords: Invariant mean, matrix transformations, sequence spaces