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On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them

Yıl 2020, Cilt: 3 Sayı: 1, 86 - 93, 10.06.2020
https://doi.org/10.33401/fujma.718298

Öz

In the paper, we have considered the real and dual bicomplex numbers separately. Firstly, we examine the dual numbers and investigate the characteristic properties of them. Then, we give the definition, feature and related concepts about bicomplex numbers. And we define the number of dual $k-$ Pell bicomplex numbers that are not found for the first time in the literature and we examine the norm and conjugate properties of these numbers. We give equations about conjugates and give also some important characteristic of these newly defined numbers, and we write the recursive correlations of these numbers. Using these relations we give some important identities such as Vajda's, Honsberger's and d'Ocagne identities.

Destekleyen Kurum

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Proje Numarası

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Kaynakça

  • [1] P. Catarino, On some identities and generating functions for k-Pell numbers, Int. J. of Math. Anal., 7(38) (2013), 1877-1884.
  • [2] P. Catarino, Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory, 19(1) (2019), 65-76.
  • [3] S. Halici, On Some Pell Polynomials. Acta Uni. Apul., 29(2012), 105-112.
  • [4] D. Alpay, M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur analysis, Springer Sci. and Business Media, (2014).
  • [5] F. Babadag, Fibonacci, Lucas numbers with dual bicomplex numbers, J. Math. Sci., 10(1-2) (2018), 161-172.
  • [6] A. T. Benjamin, S. S. Plott, J. A. Sellers, Tiling proofs of recent sum identities involving Pell numbers, Ann. Comb., 12(3) (2008), 271-278.
  • [7] M. A. Gungor, A. Cihan, On dual-hyperbolic numbers with generalized Fibonacci and Lucas numbers components, Fundam. J. Math. Appl., 2(2) (2019), 162-172, doi: 10.33401/fujma.617415.
  • [8] S. Halici, On Bicomplex Fibonacci Numbers and Their Generalization, In Models and Theories in Social Systems (pp. 509-524), Springer, Cham, (2019).
  • [9] S. Ö . Karakuş, F. K. Aksoyak, Generalized bicomplex numbers and Lie groups, Adv. Appl. Clifford Alg., 25(4) (2015), 943-963.
  • [10] M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac, Bicomplex numbers and their elementary functions, Cubo(Temuco), 14(2) (2012), 61-80.
Yıl 2020, Cilt: 3 Sayı: 1, 86 - 93, 10.06.2020
https://doi.org/10.33401/fujma.718298

Öz

Proje Numarası

-

Kaynakça

  • [1] P. Catarino, On some identities and generating functions for k-Pell numbers, Int. J. of Math. Anal., 7(38) (2013), 1877-1884.
  • [2] P. Catarino, Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory, 19(1) (2019), 65-76.
  • [3] S. Halici, On Some Pell Polynomials. Acta Uni. Apul., 29(2012), 105-112.
  • [4] D. Alpay, M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur analysis, Springer Sci. and Business Media, (2014).
  • [5] F. Babadag, Fibonacci, Lucas numbers with dual bicomplex numbers, J. Math. Sci., 10(1-2) (2018), 161-172.
  • [6] A. T. Benjamin, S. S. Plott, J. A. Sellers, Tiling proofs of recent sum identities involving Pell numbers, Ann. Comb., 12(3) (2008), 271-278.
  • [7] M. A. Gungor, A. Cihan, On dual-hyperbolic numbers with generalized Fibonacci and Lucas numbers components, Fundam. J. Math. Appl., 2(2) (2019), 162-172, doi: 10.33401/fujma.617415.
  • [8] S. Halici, On Bicomplex Fibonacci Numbers and Their Generalization, In Models and Theories in Social Systems (pp. 509-524), Springer, Cham, (2019).
  • [9] S. Ö . Karakuş, F. K. Aksoyak, Generalized bicomplex numbers and Lie groups, Adv. Appl. Clifford Alg., 25(4) (2015), 943-963.
  • [10] M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac, Bicomplex numbers and their elementary functions, Cubo(Temuco), 14(2) (2012), 61-80.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Serpil Halıcı 0000-0002-8071-0437

Şule Çürük Bu kişi benim 0000-0002-4514-6156

Proje Numarası -
Yayımlanma Tarihi 10 Haziran 2020
Gönderilme Tarihi 11 Ocak 2020
Kabul Tarihi 9 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Halıcı, S., & Çürük, Ş. (2020). On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them. Fundamental Journal of Mathematics and Applications, 3(1), 86-93. https://doi.org/10.33401/fujma.718298
AMA Halıcı S, Çürük Ş. On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them. Fundam. J. Math. Appl. Haziran 2020;3(1):86-93. doi:10.33401/fujma.718298
Chicago Halıcı, Serpil, ve Şule Çürük. “On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them”. Fundamental Journal of Mathematics and Applications 3, sy. 1 (Haziran 2020): 86-93. https://doi.org/10.33401/fujma.718298.
EndNote Halıcı S, Çürük Ş (01 Haziran 2020) On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them. Fundamental Journal of Mathematics and Applications 3 1 86–93.
IEEE S. Halıcı ve Ş. Çürük, “On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them”, Fundam. J. Math. Appl., c. 3, sy. 1, ss. 86–93, 2020, doi: 10.33401/fujma.718298.
ISNAD Halıcı, Serpil - Çürük, Şule. “On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them”. Fundamental Journal of Mathematics and Applications 3/1 (Haziran 2020), 86-93. https://doi.org/10.33401/fujma.718298.
JAMA Halıcı S, Çürük Ş. On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them. Fundam. J. Math. Appl. 2020;3:86–93.
MLA Halıcı, Serpil ve Şule Çürük. “On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them”. Fundamental Journal of Mathematics and Applications, c. 3, sy. 1, 2020, ss. 86-93, doi:10.33401/fujma.718298.
Vancouver Halıcı S, Çürük Ş. On Dual $k-$ Pell Bicomplex Numbers and Some Identities Including Them. Fundam. J. Math. Appl. 2020;3(1):86-93.

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