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On Some Properties of New Paranormed Sequence Space of Nonabsolute Type

Vatan Karakaya, Necip Şi̇mşek

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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.

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What this paper is about

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.

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Sequence space, Sequence (biology), Mathematics, Space (punctuation), Isomorphism (crystallography), Completeness (order theory), Zero-dimensional space, Dual polyhedron

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