Araştırma Makalesi
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Tribonacci-Lucas Sequence Spaces

Yıl 2023, Cilt: 13 Sayı: 1, 548 - 562, 01.03.2023
https://doi.org/10.21597/jist.1154099

Öz

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.

Kaynakça

  • 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 𝑐0 and 𝑐. Korean J. Math., 29 (1): 25-40.

Tribonacci-Lucas Dizi Uzayları

Yıl 2023, Cilt: 13 Sayı: 1, 548 - 562, 01.03.2023
https://doi.org/10.21597/jist.1154099

Öz

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.

Kaynakça

  • 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 𝑐0 and 𝑐. Korean J. Math., 29 (1): 25-40.
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Murat Karakaş 0000-0002-5174-0282

Uğurcan Şevik 0000-0003-1467-3188

Erken Görünüm Tarihi 24 Şubat 2023
Yayımlanma Tarihi 1 Mart 2023
Gönderilme Tarihi 11 Ağustos 2022
Kabul Tarihi 5 Kasım 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 13 Sayı: 1

Kaynak Göster

APA Karakaş, M., & Şevik, U. (2023). Tribonacci-Lucas Dizi Uzayları. Journal of the Institute of Science and Technology, 13(1), 548-562. https://doi.org/10.21597/jist.1154099
AMA Karakaş M, Şevik U. Tribonacci-Lucas Dizi Uzayları. Iğdır Üniv. Fen Bil Enst. Der. Mart 2023;13(1):548-562. doi:10.21597/jist.1154099
Chicago Karakaş, Murat, ve Uğurcan Şevik. “Tribonacci-Lucas Dizi Uzayları”. Journal of the Institute of Science and Technology 13, sy. 1 (Mart 2023): 548-62. https://doi.org/10.21597/jist.1154099.
EndNote Karakaş M, Şevik U (01 Mart 2023) Tribonacci-Lucas Dizi Uzayları. Journal of the Institute of Science and Technology 13 1 548–562.
IEEE M. Karakaş ve U. Şevik, “Tribonacci-Lucas Dizi Uzayları”, Iğdır Üniv. Fen Bil Enst. Der., c. 13, sy. 1, ss. 548–562, 2023, doi: 10.21597/jist.1154099.
ISNAD Karakaş, Murat - Şevik, Uğurcan. “Tribonacci-Lucas Dizi Uzayları”. Journal of the Institute of Science and Technology 13/1 (Mart 2023), 548-562. https://doi.org/10.21597/jist.1154099.
JAMA Karakaş M, Şevik U. Tribonacci-Lucas Dizi Uzayları. Iğdır Üniv. Fen Bil Enst. Der. 2023;13:548–562.
MLA Karakaş, Murat ve Uğurcan Şevik. “Tribonacci-Lucas Dizi Uzayları”. Journal of the Institute of Science and Technology, c. 13, sy. 1, 2023, ss. 548-62, doi:10.21597/jist.1154099.
Vancouver Karakaş M, Şevik U. Tribonacci-Lucas Dizi Uzayları. Iğdır Üniv. Fen Bil Enst. Der. 2023;13(1):548-62.