Some $m$th-order Difference Sequence Spaces of Generalized Means and Compact Operators

Abstract

In this paper, new sequence spaces X(r, s, t; ∆ (m) ) for X ∈ {l ∞ , c, c 0 } defined by using generalized means and difference operator of order m are introduced. It is shown that these spaces are complete normed linear spaces and the spaces c 0 (r, s, t; ∆ (m) ), c(r, s, t; ∆ (m) ) have Schauder basis. Furthermore, the α-, β-, γ-duals of these spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from X(r, s, t; ∆ (m) ) to X. Finally, some classes of compact operators on the spaces c 0 (r, s, t; ∆ (m) ) and l ∞ (r, s, t; ∆ (m) ) are characterized by using the Hausdorff measure of noncompactness.

On B(m)${B^{(m)}}$-difference sequence spaces using generalized means and compact operators

“…In this paper, an attempt is made to introduce new sequence spaces by combining generalized means and the operator ( ) ( , ) which not only include the results of Polat et al [27], Başarir and Kara [5,7] as particular case but also give sequence spaces that include Euler ( ) -di erence sequence spaces. Some recent developments on di erence sequence spaces using generalized means can be found in [16].…”