### A bounded consistency theorem for strong summabilities.

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A general theorem concerning many absolute summability methods is proved.

In this paper we introduce a new sequence space $B{V}_{\sigma}(\mathcal{M},u,p,r,\parallel \xb7,...,\xb7\parallel )$ defined by a sequence of Orlicz functions $\mathcal{M}=\left({M}_{k}\right)$ and study some topological properties of this sequence space.

In this paper we have proved a main theorem concerning the | $$\overline{N}$$ , p n; δ |k summability methods, which generalizes a result of Bor and Özarslan [3].