We have introduced a new sequence space $l(r, s, t, p ;\Delta^{ (m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{ (m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from $l(r, s, t, p; \Delta^{ (m)})$ to $l_{ \infty}, l_1$. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff 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.
Categories: math.FA