Summary: The sequence spaces

${\ell}_{\infty}\left(p\right)$,

$c\left(p\right)$ and

${c}_{0}\left(p\right)$ were introduced and studied by

*I. J. Maddox*, Proc. Camb. Philos. Soc. 64, 335–340 (1968;

Zbl 0157.43503)]. 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 it is proved that the spaces

$\lambda (u,v;p)$ and

$\lambda \left(p\right)$ are linearly isomorphic, where

$\lambda $ denotes one of the sequence spaces

${\ell}_{\infty}$,

$c$ or

${c}_{0}$. Besides this, the

$\beta $- and

$\gamma $-duals of the spaces

$\lambda (u,v;p)$ are computed and 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 the AD property and the

$f$-dual of the space

${c}_{0}(u,v;p)$ is given. 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.