Abstract
The sequence spaces ℓ ∞ ( p ) , c ( p ) and c 0 ( p ) were introduced and studied by Maddox [I.J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Cambridge Philos. Soc. 64 (1968) 335–340]. In the present paper, the sequence spaces λ ( u , v ; p ) of non-absolute type which are derived by the generalized weighted mean are defined and proved that the spaces λ ( u , v ; p ) and λ ( p ) are linearly isomorphic, where λ denotes the one of the sequence spaces ℓ ∞ , c or c 0 . Besides this, the β- and γ-duals of the spaces λ ( u , v ; p ) are computed and the basis of the spaces c 0 ( u , v ; p ) and c ( u , v ; p ) is constructed. Additionally, it is established that the sequence space c 0 ( u , v ) has AD property and given the f-dual of the space c 0 ( u , v ; p ) . Finally, the matrix mappings from the sequence spaces λ ( u , v ; p ) to the sequence space μ and from the sequence space μ to the sequence spaces λ ( u , v ; p ) are characterized.
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