SOME GEOMETRIC PROPERTIES OF DIFFERENCE SEQUENCE SPACES OF ORDER m DERIVED BY GENERALIZED MEANS AND COMPACT OPERATORS

We have introduced a new sequence space l( r,s,t,p;Delta((m))) combining by using generalized means and difference operator of order m. Some topological properties as well as geometric properties namely Banach-Saks property of type p and uniform Opial property have been studied. Furthermore, the alpha-, beta-, gamma- duals of this space are computed and also obtained necessary and sufficient conditions for some matrix transformations from l(r,s,t,p;Delta((m))) to l(infinity), l(1). Finally, we obtained some identities or estimates for operator norms and measure of noncompactness of some matrix operators on the BK space l(p)(r,s,t;Delta((m))) by applying the Hausdorff measure of noncompactness.