Abstract
We introduce some new generalized sequence space related to the space ℓ(p). Furthermore we investigate some topological properties as the completeness, the isomorphism, and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute α‐, β‐, and γ‐duals of this space and characterize certain matrix transformations on this sequence space.
Highlights
In studying the sequence spaces, especially, to obtain new sequence spaces, in general, the matrix domain μA of an infinite matrix A defined by μA {x xk ∈ w : Ax ∈ μ} is used
The sequence space λ, p is the complete linear metric space with respect to paranorm defined by hx
The linearity of λ, p with respect to the coordinatewise addition and scalar multiplication follows from the following inequalities which are satisfied for x, t ∈ λ, p see, 15 :
Summary
In studying the sequence spaces, especially, to obtain new sequence spaces, in general, the matrix domain μA of an infinite matrix A defined by μA {x xk ∈ w : Ax ∈ μ} is used. In 1 , Mursaleen and Noman constructed new sequence spaces by using matrix domain over a normed space. They studied some topological properties and inclusion relations of these spaces. We generalize the normed sequence spaces defined by Mursaleen and Noman 1 to the paranormed spaces. By using the matrix domain over the paranormed spaces, many authors have defined new sequence spaces.
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