In this work, we define new sequence spaces by combining generalized weighted mean and difference operator. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the α− , β− and γ− duals, and obtain bases for these sequence spaces. Finally, necessary and sufficient conditions on an infinite matrix belonging to the classes (c (u, v, ∆) : ℓ∞) and (c (u, v, ∆) : c) are established.2000 Mathematics Subject Classification. 46A05, 46A35, 46A45. Key words and phrases. Difference sequence space, generalized weighted mean, AK and AD properties, the α−, β− and γ− duals and bases of sequences, matrix mappings.
The main purpose of the present paper is to study of some new Pascal sequence spaces p ∞ , p c and p 0. New Pascal sequence spaces p ∞ , p c and p 0 are found as BK-spaces and it is proved that the spaces p ∞ , p c and p 0 are linearly isomorphic to the spaces l ∞ , c and c 0 respectively. Afterward, α-, β-and γ-duals of these spaces p c and p 0 are computed and their bases are consructed. Finally, matrix the classes (p c : l p) and (p c : c) have been characterized.
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