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Journals / Mathematical Sciences and Applications E-Notes / 2019 / Cilt: 7 - Sayı: 2

On the Difference Sequence Space `p(Tˆq)

Pınar ZENGIN ALP
Merve İLKHAN
Pages
161–173
DOI
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AI Summary & Key Takeaways

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

Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes (`p(Tˆq ), λ) or (λ, `p(Tˆq )), where λ ∈ {`1, c0, c, `∞}.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we introduce a new matrix Tˆq = (tˆ q nk) by tˆ q nk =    qn Qn tn , k = n qk Qn tk − qk+1 Qn 1 tk+1 , k n. where tk > 0 for all n ∈ N and (tn) ∈ c\c0.
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Key Findings & Data:By using the matrix Tˆq , we introduce the sequence space `p(Tˆq ) for 1 ≤ p ≤ ∞.
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Conclusion & Impact:Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes (`p(Tˆq ), λ) or (λ, `p(Tˆq )), where λ ∈ {`1, c0, c, `∞}.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Özet

In this study, we introduce a new matrix Tˆq = (tˆ q nk) by tˆ q nk =    qn Qn tn , k = n qk Qn tk − qk+1 Qn 1 tk+1 , k n. where tk > 0 for all n ∈ N and (tn) ∈ c\c0. By using the matrix Tˆq , we introduce the sequence space `p(Tˆq ) for 1 ≤ p ≤ ∞. In addition, we give some theorems on inclusion relations associated with `p(Tˆq ) and find the α-, β-, γ- duals of this space. Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes (`p(Tˆq ), λ) or (λ, `p(Tˆq )), where λ ∈ {`1, c0, c, `∞}.

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Cite This Article

ALP, P. Z., İLKHAN, M. (2019). On the Difference Sequence Space `p(Tˆq). Mathematical Sciences and Applications E-Notes, Cilt: 7 - Sayı: 2, 161–173. https://ajindex.com/articles/283475

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