Abstract
The new sequence spaces $X(r,s,t;\Delta)$ for $X\in\{l_{\infty}, c, c_{0}\}$ have been defined by using generalized means and difference operator. In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on some new difference sequence spaces $X(r,s,t;\Delta )$ where $X\in\{l_{\infty}, c, c_{0},l_{p}\}$ ( $1\leq{p}<\infty$ ), as derived by using generalized means. Further, we find the necessary and sufficient conditions for such operators to be compact by applying the Hausdorff measure of noncompactness. Finally, as applications we characterize some classes of compact operators between these new difference sequence spaces and some other BK-spaces.
Highlights
The new sequence spaces X(r, s, t; ) for X ∈ {l∞, c, c0} have been defined by using generalized means and difference operator
Afterwards, many authors have introduced and studied some new sequence spaces defined by using the difference operator
In [ ] Ahmad and Mursaleen, in [ ] Colak and Et, in [ ] Basar and Altay, in [ ] Orhan, in [ ] Polat and Altay, in [ ] Aydin and Basar, and in [ ] Basar and Altay have introduced and studied some new sequence spaces defined by using a difference operator
Summary
The new sequence spaces X(r, s, t; ) for X ∈ {l∞, c, c0} have been defined by using generalized means and difference operator. Afterwards, many authors have introduced and studied some new sequence spaces defined by using the difference operator. In Manna et al [ ] have introduced new sequence spaces defined by using both the generalized means and the difference operator.
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