Maddox defined the sequence spaces l(infinity)(p), c(p) and c(0)(p) in [Proc. Camb. Philos. Soc. 64 (1968) 335, Quart. J. Math. Oxford (2) 18 (1967) 345]. In the present paper, the sequence spaces a(0)(r)(u,p) and a(c)(r)(u,p) of non-absolute type have been introduced and proved that the spaces a(0)(r)(u,p) and a(c)(r)(u,p) are linearly isomorphic to the spaces c(0)(p) and c(p), respectively. Besides this, the alpha-, beta- and gamma-duals of the spaces a(0)(r)(u,p) and a(c)(r)(u,p) have been computed and their basis have been constructed. Finally, a basic theorem has been given and later some matrix mappings from a(0)(r)(u,p) to the some sequence spaces of Maddox and to some new sequence spaces have been characterized. (C) 2003 Elsevier Inc. All rights reserved.