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In this paper we introduce \beta -duals and \gamma -duals of the sequence spaces l_{\infty}(\triangle^{m}) , c(\triangle^{m}) , (m\in N) where for instance l_{\infty}(\triangle^{m})=\{x=(x_{k}) : (\triangle^{m}x_{k})\in l_{\infty}\} , and we characterize some matrix classes related with these sequence spaces. This study generalizes some results of K_{1}zmaz[4] in special cases.

The definition of the pα-, pβ-and pγ -duals of a sequence space was defined by Et [Internat. J. Math. Math. Sci. 24 (2000) 785-791]. In this paper we compute pα-and N-duals of the sequence spaces ∆ m v (X) for X = ∞ , c and c 0 , and compute β-and γ -duals of the sequence spaces ∆ m v (X) for X = ∞ , c and c 0 .  2004 Elsevier Inc. All rights reserved.

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