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Some paranormed sequence spaces of non-absolute type derived by weighted mean
(Academic Press Inc Elsevier Science, 2006) Altay, Bilal; Bapar, Feyzi
The sequence spaces l(infinity) (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 lambda(u, v; p) of non-absolute type which are derived by the generalized weighted mean are defined and proved that the spaces lambda(u, v; p) and lambda(p) are linearly isomorphic, where. denotes the one of the sequence spaces l(infinity), c or c(0). Besides this, the beta- and gamma-duals of the spaces lambda(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 lambda(u, v; p) to the sequence space mu and from the sequence space mu to the sequence spaces lambda(u, v; p) are characterized. (c) 2005 Elsevier Inc. All rights reserved.