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Journals / Sakarya University Journal of Science / 2026 / Volume: 23 Issue: 4

A Note On The Series Space |N ̅_p^θ |(μ)

Fadime Gökçe(PAMUKKALE UNIVERSITY)0000-0003-1819-3317
Pages
—
Publication Date
2019-08-01
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AI Summary & Key Takeaways

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

The main purpose of this paper is to determine the $ \alpha- $ , $ \beta- $ and $ \gamma $ _ duals of the space and to show that it is linearly isomorphic to the Maddox’s space $ l(\mu) $.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The series space $\left\vert \bar{N}_{p}^{\theta }\right\vert \left( \mu \right) $ has recently been introduced and studied by Gökçe and Sarıgöl [ 1 ].
📊
Key Findings & Data:The series space $\left\vert \bar{N}_{p}^{\theta }\right\vert \left( \mu \right) $ has recently been introduced and studied by Gökçe and Sarıgöl [ 1 ].
💡
Conclusion & Impact:The main purpose of this paper is to determine the $ \alpha- $ , $ \beta- $ and $ \gamma $ _ duals of the space and to show that it is linearly isomorphic to the Maddox’s space $ l(\mu) $.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Absolute summability · Sequence spaces · Weighted mean

Abstract

The series space $\left\vert \bar{N}_{p}^{\theta }\right\vert \left( \mu \right) $ has recently been introduced and studied by Gökçe and Sarıgöl [ 1 ]. The main purpose of this paper is to determine the $ \alpha- $ , $ \beta- $ and $ \gamma $ _ duals of the space and to show that it is linearly isomorphic to the Maddox’s space $ l(\mu) $.

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Cite This Article

Gökçe, F. (2019). A Note On The Series Space |N ̅_p^θ |(μ). Sakarya University Journal of Science, Volume: 23 Issue: 4. https://doi.org/10.16984/saufenbilder.486492

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References (2)

  1. F. Gökçe and M.A. Sarıgöl, “A new series space |N ̅_p^θ |(μ) and matrix operatör with applications”, Kuwait Journal of Science, vol. 45, no. 4, pp. 1-8, 2018.[2] I.J. Maddox,, “Some properties of paranormed sequence spaces,” Journal of the London Mathematical Society, vol. 1, pp. 316–322, 1969.[3] I.J. Maddox, “Paranormed sequence spaces Generated by infinite matrices,”Mathematical Proceedings of the Cambridge Philosophical Society, vol. 64, pp. 335–340, 1968.[4] I.J. Maddox, “Spaces of strongly summable sequences,” The Quarterly Journal of Mathematics, vol. 18, pp. 345–355, 1967.[5] H. Bor, “On |N ̅,p_n |_k summability factors of infinite series,” Tamkang J. Math, vol. 16, no. 1, pp. 13– 20, 1985.[6] T.M. FLett,, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proc. London Math. Soc., vol. 7, pp. 113-141, 1957.[7] M.A. Sarıgöl, “Spaces of series summable by absolute Cesàro and matrix operators,” Comm. Math. Appl., vol. 7, pp. 11–22, 2016.[8] M.A. Sarıgöl, “Norms and compactness of operators on absolute weighted mean, summable series,” Kuwait Journal of Science, vol. 43, no. 4, pp. 68–74, 2016.[9] M.A. Sarıgöl, “An inequality for matrix operators and its applications.,” J. Classical Anal, vol. 2, pp. 145–150, 2013. [10] M.A. Sarıgöl, “Matrix transformations on fields of absolute weighted mean summability,” Studia Scientiarum Mathematicarum Hungarica., vol. 48, no. 3, pp. 331–341, 2011.[11] M.A. Sarıgöl, “On local properties of factored Fourier series.,” Appl. Math. Comp., vol. 216, no. 3, pp. 3386–3390, 2010.[12] K.G. Grosse-Erdmann,, “Matrix transformations between the sequence spaces of Maddox.,” Journal of Mathematical Analysis and Applications, vol. 180, pp. 223–238, 1993.
  2. F. Gökçe and M.A. Sarıgöl, “A new series space |N ̅_p^θ |(μ) and matrix operatör with applications”, Kuwait Journal of Science, vol. 45, no. 4, pp. 1-8, 2018.[2] I.J. Maddox,, “Some properties of paranormed sequence spaces,” Journal of the London Mathematical Society, vol. 1, pp. 316–322, 1969.[3] I.J. Maddox, “Paranormed sequence spaces Generated by infinite matrices,”Mathematical Proceedings of the Cambridge Philosophical Society, vol. 64, pp. 335–340, 1968.[4] I.J. Maddox, “Spaces of strongly summable sequences,” The Quarterly Journal of Mathematics, vol. 18, pp. 345–355, 1967.[5] H. Bor, “On |N ̅,p_n |_k summability factors of infinite series,” Tamkang J. Math, vol. 16, no. 1, pp. 13– 20, 1985.[6] T.M. FLett,, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proc. London Math. Soc., vol. 7, pp. 113-141, 1957.[7] M.A. Sarıgöl, “Spaces of series summable by absolute Cesàro and matrix operators,” Comm. Math. Appl., vol. 7, pp. 11–22, 2016.[8] M.A. Sarıgöl, “Norms and compactness of operators on absolute weighted mean, summable series,” Kuwait Journal of Science, vol. 43, no. 4, pp. 68–74, 2016.[9] M.A. Sarıgöl, “An inequality for matrix operators and its applications.,” J. Classical Anal, vol. 2, pp. 145–150, 2013. [10] M.A. Sarıgöl, “Matrix transformations on fields of absolute weighted mean summability,” Studia Scientiarum Mathematicarum Hungarica., vol. 48, no. 3, pp. 331–341, 2011.[11] M.A. Sarıgöl, “On local properties of factored Fourier series.,” Appl. Math. Comp., vol. 216, no. 3, pp. 3386–3390, 2010.[12] K.G. Grosse-Erdmann,, “Matrix transformations between the sequence spaces of Maddox.,” Journal of Mathematical Analysis and Applications, vol. 180, pp. 223–238, 1993.