On the mth order difference sequence space of generalized weighted mean and compact operators

Abstract

In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l(u, v, p; Delta((m))), which consist of the sequences whose generalized weighted Delta((m))-difference means are in the linear space l(p) defined by I.J.Maddox. Also, we determine the basis of this space and compute its alpha-, beta- and gamma-duals. Further, we give the characterization of the classes of matrix mappings from l(u, v, p, Delta((m))) to l(infinity), c, and c(o). Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space l(p)(u, v, Delta((m))) (1 <= p < infinity).