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Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 10 - Sayı: 10

Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces

Serkan Demiri
Hacer Bilgin Ellidokuzoğlu
Pages
144–152
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, the classes of matrices(c0(Lˆ, ∆) : µ) and (c(Lˆ, ∆) : µ) have been characterized, where µ is one of the sequence spaces `∞, c and c0 andderives the other characterizations for the special cases of µ.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Karakas¸ and Karabudak [22], introduced the Lucas sequence spaces X(E) and studied their someproperties.
📊
Key Findings & Data:The main purpose of this study is to introduce the Lucas difference sequence spaces c0(Lˆ, ∆) and c(Lˆ, ∆)by using the Lucas sequence.
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Conclusion & Impact:Finally, the classes of matrices(c0(Lˆ, ∆) : µ) and (c(Lˆ, ∆) : µ) have been characterized, where µ is one of the sequence spaces `∞, c and c0 andderives the other characterizations for the special cases of µ.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Karakas¸ and Karabudak [22], introduced the Lucas sequence spaces X(E) and studied their someproperties. The main purpose of this study is to introduce the Lucas difference sequence spaces c0(Lˆ, ∆) and c(Lˆ, ∆)by using the Lucas sequence. Also, we prove that the spaces c0(Lˆ, ∆) and c(Lˆ, ∆), are linearly isomorphic to spacesc0 and c, respectively. Besides this, the α−, β− and γ−duals of this spaces have been computed, their bases havebeen constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices(c0(Lˆ, ∆) : µ) and (c(Lˆ, ∆) : µ) have been characterized, where µ is one of the sequence spaces `∞, c and c0 andderives the other characterizations for the special cases of µ.

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Cite This Article

Demiri, S., Ellidokuzoğlu, H. B. (2022). Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces. Turkish Journal of Mathematics and Computer Science, Cilt: 10 - Sayı: 10, 144–152. https://ajindex.com/articles/609159

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