Tribonacci-Lucas Dizi Uzayları

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.

Anahtar Kelimeler:

Tribonacci-Lucas sayıları, Dizi uzayı, Schauder bazı, Köthe-Toeplitz dualleri, Matris dönüşümü, Düzgün konvekslik

Tribonacci-Lucas Sequence Spaces

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.

Keywords:

Tribonacci-Lucas numbers, Squence space, Schauder basis, Köthe-Toeplitz duals, Matrix transformation, Uniform convexity,

PDF

___

Başar, F. (2011). Summability Theory and its Applications. Bentham Science Publishers. İstanbul.
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.
Candan, M., Kara, EE. (2015). A Study of Topological and Geometrical Characteristics of New Banach Sequence Spaces. Gulf J. Math., 3 (4): 67-84.
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.
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.
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.
Gökçe, F. (2022). Absolute Lucas Spaces with Matrix and Compact Operators. Math. Sci. Appl. Enotes, 10 (1): 27-44.
Gökçe, F., Sarıgöl, MA. (2020). Some Matrix and Compact Operators of the Absolute Fibonacci Series Spaces. Kragujevac J. Math., 44 (2): 273-286.
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.
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.
James, CR. (1972). Super Reflexive Spaces with Bases. Pasific J. Math., 41: 409-419.
Kamthan PK, Gupta M, 1981. Sequence Spaces and Series. Marcel Dekker Inc. New York and Basel.
Kara, EE. (2013). Some Topological and Geometrical Properties of New Banach Sequence Spaces. J. Inequal. Appl., 38: https://doi.org/10.1186/1029-242X-2013-38
Kara, EE., Başarır, M. (2012). An Application of Fibonacci Numbers into Infinite Toeplitz Matrices. Caspian J. Math. Sci., 1 (1): 43-47.
Kara, EE., İlkhan, M. (2015). On Some Banach Sequence Spaces Derived by a New Band Matrix. British J. Math. Comput. Sci., 9 (2): 141-159.
Kara, EE., İlkhan, M. (2016). Some Properties of Generalized Fibonacci Sequence Spaces. Linear and Multilinear Algebra, 64 (11): 2208-2223.
Karakaş, M. (2021). Some Inclusion Results for the New Tribonacci-Lucas Matrix. BEU J. Sci. Tech., 11 (2): 76-81.
Karakaş, M., Karakaş, A. (2017). New Banach Sequence Spaces that is Defined by the aid Of Lucas Numbers. Journal of the Institute of Science and Technology, 7 (4): 103-111.
Karakaş, M., Karakaş, A. (2018). A Study on Lucas Difference Sequence Spaces  ˆ  ,  p l E r s and l Eˆ r, s  . Maejo Int. J. Sci. Tech., 12 (1): 70-78.
Köthe, G., Toeplitz, O. (1934). Linear Raume mit Unendlich Vielen Koordinaten and Ringe Unenlicher Matrizen. J. Rreine Angew. Math., 171: 193-226.
Mursaleen M, Noman AK, 2010. On the Spaces of   Convergent and Bounded Sequences. Thai J. Math., 8: 311-329.
Mursaleen, M., Noman, AK. (2011). On Some New Sequence Spaces of Non-Absolute Type Related to the Spaces p and  I. Filomat, 25: 33-51.
Stieglitz, M., Tietz, H. (1977). Matrixtransformationen von Folgenraumen eine Ergebnisübersicht. Math. Z., 154: 1-16.
Wilansky, A. (1984). Summability Through Functional Analysis. North-Holland Mathematics Studies Vol. 85. Elseiver. Amsterdam.
Yaying, T., Hazarika, B. (2020). On Sequence Spaces Defined by the Domain of a Regular Tribonacci Matrix. Math. Slovaca, 70 (3): 697-706.
Yaying, T., Hazarika, B., Mohiuddine, SA. (2021). On Difference Sequence Spaces of Fractional Order Involving Padovan Numbers, Asian-European J. Math., 14 (6): 1-24.
Yaying, T., Kara, MI. (2021). On Sequence Spaces Defined by the Domain of Tribonacci Matrix in ?0 and ?. Korean J. Math., 29 (1): 25-40.