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On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces

Yıl 2024, Cilt: 7 Sayı: 2, 80 - 87
https://doi.org/10.33434/cams.1442975

Öz

In this work, we give some results about the basic properties of the vector-valued Fibonacci sequence spaces. In general, sequence spaces with Banach space-valued cannot have a Schauder Basis unless the terms of the sequences are complex or real terms. Instead, we defined the concept of relative basis in \cite{yy2} by generalizing the definition of a basis in Banach spaces. Using this definition, we have characterized certain important properties of vector-term Fibonacci sequence spaces, such as separability, Dunford-Pettis Property, approximation property, Radon-Riesz Property and Hahn-Banach extension property.

Kaynakça

  • [1] Y. Yilmaz, Relative bases in Banach spaces, Nonlinear Anal., 71 (2009), 2012–2021.
  • [2] E. E. Kara, M. İlkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11) (2016), 2208–2223.
  • [3] T. Koshy, Fibonacci and Lucus Numbers with Applications, Wiley, New York, 2001.
  • [4] E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., 38 (2013), 1–15.
  • [5] S. Ercan, Ç. A. Bektaş, Some topological and geometric properties of a new BK-space derived by using regular matrix of Fibonacci numbers, Linear Multilinear Algebra, 65(5) (2017), 909–921.
  • [6] M. Candan, Some characteristics of matrix operators on generalized Fibonacci weighted difference sequence space, Symmetry, 14(7) (2022), 1283.
  • [7] R. E. Megginson, An Introduction to Banach Space Theory, Springer-Verlag, New York, 1998.
  • [8] A. Grothendieck, Sur les applications lineaires faiblement compactness d’espaces du type C(K), Canad. J. Math., 5 (1953), 129-173.
  • [9] D. Hilbert, Grundzii.ge einer allgemeinen Theorie der linearen lntegralgleichungen, IV, Nachr. Kgl. Gesells. Wiss. Gottingen Math.Phys. Kl., (1906), 157-227.
  • [10] R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc., 48 (1940), 516-541.
  • [11] J. Radon, Theorie und Anwendungen der absalut additiven Mengenfunktionen, S.-B. Akad. Wiss. Wien, 122 (1913), 1295-1438.
  • [12] F. Riesz, Sur la convergence en moyenne, I, Acta Sci. Math., 4 (1928-1929), 58-64.
  • [13] F. Riesz, Sur la convergence en moyenne, II, Acta Sci. Math., 4 (1928-1929), 182-185.
  • [14] M. I. Kadets, On strong and weak convergence, Dokl. Akad. Nauk SSSR, 122 (1958), 13-16. (Russian)
  • [15] V. Klee, Mappings into normed linear spaces, Fund. Math., 49 (1960/61), 25-34.
  • [16] V. Klee, A proof of the topological equivalence of all separable infinite-dimensional Banach spaces, Functional Anal. Appl., 1 (1967), 53-62.
Yıl 2024, Cilt: 7 Sayı: 2, 80 - 87
https://doi.org/10.33434/cams.1442975

Öz

Kaynakça

  • [1] Y. Yilmaz, Relative bases in Banach spaces, Nonlinear Anal., 71 (2009), 2012–2021.
  • [2] E. E. Kara, M. İlkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11) (2016), 2208–2223.
  • [3] T. Koshy, Fibonacci and Lucus Numbers with Applications, Wiley, New York, 2001.
  • [4] E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., 38 (2013), 1–15.
  • [5] S. Ercan, Ç. A. Bektaş, Some topological and geometric properties of a new BK-space derived by using regular matrix of Fibonacci numbers, Linear Multilinear Algebra, 65(5) (2017), 909–921.
  • [6] M. Candan, Some characteristics of matrix operators on generalized Fibonacci weighted difference sequence space, Symmetry, 14(7) (2022), 1283.
  • [7] R. E. Megginson, An Introduction to Banach Space Theory, Springer-Verlag, New York, 1998.
  • [8] A. Grothendieck, Sur les applications lineaires faiblement compactness d’espaces du type C(K), Canad. J. Math., 5 (1953), 129-173.
  • [9] D. Hilbert, Grundzii.ge einer allgemeinen Theorie der linearen lntegralgleichungen, IV, Nachr. Kgl. Gesells. Wiss. Gottingen Math.Phys. Kl., (1906), 157-227.
  • [10] R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc., 48 (1940), 516-541.
  • [11] J. Radon, Theorie und Anwendungen der absalut additiven Mengenfunktionen, S.-B. Akad. Wiss. Wien, 122 (1913), 1295-1438.
  • [12] F. Riesz, Sur la convergence en moyenne, I, Acta Sci. Math., 4 (1928-1929), 58-64.
  • [13] F. Riesz, Sur la convergence en moyenne, II, Acta Sci. Math., 4 (1928-1929), 182-185.
  • [14] M. I. Kadets, On strong and weak convergence, Dokl. Akad. Nauk SSSR, 122 (1958), 13-16. (Russian)
  • [15] V. Klee, Mappings into normed linear spaces, Fund. Math., 49 (1960/61), 25-34.
  • [16] V. Klee, A proof of the topological equivalence of all separable infinite-dimensional Banach spaces, Functional Anal. Appl., 1 (1967), 53-62.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Articles
Yazarlar

Yılmaz Yılmaz 0000-0003-1484-782X

Seçkin Yalçın 0000-0002-1673-3319

Erken Görünüm Tarihi 5 Haziran 2024
Yayımlanma Tarihi
Gönderilme Tarihi 26 Şubat 2024
Kabul Tarihi 6 Mayıs 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 7 Sayı: 2

Kaynak Göster

APA Yılmaz, Y., & Yalçın, S. (2024). On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces. Communications in Advanced Mathematical Sciences, 7(2), 80-87. https://doi.org/10.33434/cams.1442975
AMA Yılmaz Y, Yalçın S. On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces. Communications in Advanced Mathematical Sciences. Haziran 2024;7(2):80-87. doi:10.33434/cams.1442975
Chicago Yılmaz, Yılmaz, ve Seçkin Yalçın. “On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces”. Communications in Advanced Mathematical Sciences 7, sy. 2 (Haziran 2024): 80-87. https://doi.org/10.33434/cams.1442975.
EndNote Yılmaz Y, Yalçın S (01 Haziran 2024) On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces. Communications in Advanced Mathematical Sciences 7 2 80–87.
IEEE Y. Yılmaz ve S. Yalçın, “On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces”, Communications in Advanced Mathematical Sciences, c. 7, sy. 2, ss. 80–87, 2024, doi: 10.33434/cams.1442975.
ISNAD Yılmaz, Yılmaz - Yalçın, Seçkin. “On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces”. Communications in Advanced Mathematical Sciences 7/2 (Haziran 2024), 80-87. https://doi.org/10.33434/cams.1442975.
JAMA Yılmaz Y, Yalçın S. On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces. Communications in Advanced Mathematical Sciences. 2024;7:80–87.
MLA Yılmaz, Yılmaz ve Seçkin Yalçın. “On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces”. Communications in Advanced Mathematical Sciences, c. 7, sy. 2, 2024, ss. 80-87, doi:10.33434/cams.1442975.
Vancouver Yılmaz Y, Yalçın S. On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces. Communications in Advanced Mathematical Sciences. 2024;7(2):80-7.

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