Generalization of the sequence space derived by weighted mean

Abstract: The sequence space 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 of non-absolute type which is derived by the generalized weighted mean is defined and proved that the spaces and are linearly isomorphic. Besides this, the β- and γ-duals of the space are computed and the basis of that space is constructed. Further, it is established that the sequence space has AD property and given f-dual of the space . Finally, the matrix mappings from the sequence spaces to the sequence space μ and from the sequence space μ to the sequence space are characterized. [Copyright &y& Elsevier]