On the B-difference sequence space derived by generalized weighted mean and compact operators

Abstract

In the present paper, by using generalized weighted mean and difference matrixB,weintroduce the paranormed sequence space (u,v,p;B)which consist of all sequenceswhose generalized weightedB-difference means are in the linear space (p)introducedbyI.J.Maddox.Also,wegivethebasisofthisspaceandcomputeitsα-,β-andγ-duals.Further, we characterize the classes of matrix mappings from (u,v,p;B)to ∞,candc0.Finally, we apply the Hausdorff measure of noncompactness to characterize some classesof compact operators given by matrices on the space p(u,v;B)(1 p<∞).