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Journals / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2023 / Cilt: 13 - Sayı: 1

Tribonacci-Lucas Sequence Spaces

Tribonacci-Lucas Dizi Uzayları

Murat KARAKAŞ
Uğurcan ŞEVİK
Pages
548–562
Publication Date
2023-03-01
DOI
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AI Summary & Key Takeaways

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

Finally, we examine whether our space has geometric properties such as uniform convexity, strict convexity, and superreflexivity.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we basically define new sequence spaces using Tribonacci-Lucas numbers.
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Key Findings & Data:Then, we give some inclusion relations by examining some topological properties of these spaces.
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Conclusion & Impact:Finally, we examine whether our space has geometric properties such as uniform convexity, strict convexity, and superreflexivity.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tribonacci-Lucas sayıları · Dizi uzayı · Schauder bazı

Abstract

In this work, we basically define new sequence spaces using Tribonacci-Lucas numbers. Then, we give some inclusion relations by examining some topological properties of these spaces. We also characterize some matrix classes by calculating the Köthe-Toeplitz duals of our space. Finally, we examine whether our space has geometric properties such as uniform convexity, strict convexity, and superreflexivity.

Özet

Bu araştırmada, temel olarak Tribonacci-Lucas sayılarını kullanarak yeni dizi uzayları tanımlıyoruz. Daha sonra bu uzayın bazı topolojik özelliklerini inceleyerek, bazı kapsama bağıntıları veriyoruz. Ayrıca uzayımızın Köthe-Toeplitz duallerini hesaplayarak, bazı matris sınıflarını karakterize ediyoruz. Son olarak, uzayımızın düzgün konvekslik, kesin konvekslik, süper yansımalılık gibi geometrik özelliklere sahip olup olmadığını inceliyoruz.

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Cite This Article

KARAKAŞ, M., ŞEVİK, U. (2023). Tribonacci-Lucas Sequence Spaces. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 13 - Sayı: 1, 548–562. https://ajindex.com/articles/886432

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References (13)

  1. Başar, F. (2011). Summability Theory and its Applications. Bentham Science Publishers.
  2. İstanbul.
  3. Başarır, M., Başar, F., Kara, EE. (2016). On the Spaces of Fibonacci Difference Absolutely p- Summable, Null and Convergent Sequences. Sarajevo J. Math., 12 (25): 167-182.
  4. Candan, M., Kara, EE. (2015). A Study of Topological and Geometrical Characteristics of New Banach Sequence Spaces. Gulf J. Math., 3 (4): 67-84.
  5. Catalani, M. (2002). Identities for Tribonacci-related Sequences. Cornell University Library. arXiv: 0209179. Chandra, P., Tripathy, BC. (2002). On Generalised Köthe-Toeplitz Duals of Some Sequence Spaces. Indian J. Pure Appl. Math., 33: 1301-1306.
  6. Chidume, CE., (1965). Geometric Properties of Banach Spaces and Non-linear Iterations. Lecture Notes in Mathematics. Springer-Verlag. Berlin. Choudary, B., Nanda, S. (1989). Functional Analysis with Applications. Wiley Eastern Limited. New Delhi. Dağlı, MC., Yaying, T. (2022). Some new Paranormed Sequence Spaces Derived by Regular Tribonacci Matrix. The Journal of Analysis, https://doi.org/10.1007/s41478-022-00442-w.
  7. Diestel, J. (1976). Geometry of Banach Spaces-Selected Topics. Lecture notes in Mathematics. Vol. 485. Springer-Verlag. Berlin. Ercan, S., Bektaş, Ç. (2017). Some Topological and Geometric Properties of a New BK-Space Derived by Using Regular Matrix of Fibonacci Numbers. Linear and Multilinear Algebra, 65 (5): 909- 921. Feinberg, M. (1963). Fibonacci-Tribonacci. The Fibonacci Quarterly, 1 (3): 70 – 74. Frontczak, R. (2018). Sums of Tribonacci and Tribonacci-Lucas Numbers. International Journal of Mathematical Analysis, 12 (1): 19-24.
  8. Gökçe, F. (2022). Absolute Lucas Spaces with Matrix and Compact Operators. Math. Sci. Appl. Enotes, 10 (1): 27-44.
  9. Gökçe, F., Sarıgöl, MA. (2020). Some Matrix and Compact Operators of the Absolute Fibonacci Series Spaces. Kragujevac J. Math., 44 (2): 273-286.
  10. İlkhan, M., Kara., Kara, EE. (2021). Matrix Transformations and Compact Operators on Catalan Sequence Spaces. J. Math. Anal. Appl., 498 (1): 124925. İlkhan, M., Kara, EE. (2019). A New Banach Space Defined by Euler Totient Matrix Operator. Operators and Matrices, 13 (2): 527-544.
  11. İlkhan, M., Şimşek, N., Kara, EE. (2021). A New Regular Infinite Matrix Defined by Jordan Totient Function and its Matrix Domain in p. Math. Meth. Appl. Sci., 44 (9): 7622-7633.
  12. James, CR. (1972). Super Reflexive Spaces with Bases. Pasific J. Math., 41: 409-419.
  13. Kamthan PK, Gupta M, 1981. Sequence Spaces and Series. Marcel Dekker In