Abstract
Maddox defined the sequence spaces ℓ ∞( 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 α-, β- and γ-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.
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