Generalization of the sequence space ℓ(p) derived by weighted mean

The sequence space ℓ(p) was introduced and studied by Maddox [I.J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford (2) 18 (1967) 345–355]. In the present paper, the sequence spaces ℓ(u,v;p) of non-absolute type which is derived by the generalized weighted mean is defined and proved that the spaces ℓ(u,v;p) and ℓ(p) are linearly isomorphic. Besides this, the β- and γ-duals of the space ℓ(u,v;p) are computed and the basis of that space is constructed. Further, it is established that the sequence space ℓp(u,v) has AD property and given f-dual of the space ℓp(u,v). Finally, the matrix mappings from the sequence spaces ℓ(u,v;p) to the sequence space μ and from the sequence space μ to the sequence space ℓ(u,v;p) are characterized.