Araştırma Makalesi
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Yıl 2022, Cilt: 71 Sayı: 1, 153 - 164, 30.03.2022
https://doi.org/10.31801/cfsuasmas.704435

Öz

Kaynakça

  • Aydin, F. T., Hyperbolic Fibonacci sequence, Universal Journal of Mathematics and Applications, 2(2) (2019), 59-64. https://doi.org/10.32323/ujma.473514
  • Bala, A., Verma, V., Some properties of bi-variate bi-periodic Lucas polynomials, Annals of the Romanian Society for Cell Biology, 25(4) (2021), 8778-8784. https://www.annalsofrscb.ro/index.php/journal/article/view/3598.
  • Bilgici, G., Two generalizations of Lucas sequence, Applied Mathematics and Computation, 245 (2014), 526-538. https://doi.org/10.1016/j.amc.2014.07.111.
  • Catoni, F., Boccaletti, R., Cannata, R., Catoni, V., Nichelatti, E., Zampatti, P., The Mathematics of Minkowski Space-Time, Birkhauser, Basel, 2008.
  • Dikmen, C.M., Hyperbolic Jacobsthal Numbers, Asian Research Journal of Mathematics, (2019) 1-9. https://doi.org/10.9734/arjom/2019/v15i430153
  • Edson, M., Yayenie, O., A new generalization of Fibonacci sequences and extended Binet’s formula, Integers, 9(A48) (2009), 639-654. https://doi.org/10.1515/INTEG.2009.051
  • Gargoubi, H., Kossentini, S., f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebr., 26(4) (2016), 1211-1233. https://doi.org/10.1007/s00006-016-0644-3
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY, 2001.
  • Khadjiev, D., Goksal Y., Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space, Adv. Appl. Clifford Algebr., 26 (2016), 645-668. https://doi.org/10.1007/s00006-015-0627-9
  • Khrennikov, A., Segre, G., An Introduction to Hyperbolic Analysis, arxiv, 2005. http://arxiv.org/abs/math-ph/0507053v2.
  • Motter, A. E, Rosa, A. F., Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1) (1998), 109-128.
  • Sobczyk, G., The hyperbolic number plane, The College Mathematics Journal, 26(4) (1995), 268-280.
  • Soykan, Y., On hyperbolic numbers with generalized Fibonacci numbers components, preprint, (2019).
  • Soykan, Y., Gocen, M., Properties of hyperbolic generalized Pell numbers, Notes on Number Theory and Discrete Mathematics, 26(4) (2020), 136-153. https://doi.org/10.7546/nntdm.2020.26.4.136-153
  • Tan, E., Leung, H.H., Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences, Advances in Difference Equations, 2020.1 (2020), 1-11. https://doi.org/10.1186/s13662-020-2507-4
  • Tasyurdu, Y., Hyperbolic Tribonacci and Tribonacci-Lucas sequences, International Journal of Mathematical Analysis, 13(12) (2019), 565-572. https://doi.org/10.12988/ijma.2019.91167
  • Verma, V., Bala, A., On properties of generalized bi-variate bi-periodic Fibonacci polynomials, International Journal of Advanced Science and Technology, 29(3) (2020), 8065-8072.
  • Yayenie, O., A note on generalized Fibonacci sequence, Applied Mathematics and Computation, 217(12) (2011), 5603-5611. https://doi.org/10.1016/j.amc.2010.12.038

Split complex bi-periodic Fibonacci and Lucas numbers

Yıl 2022, Cilt: 71 Sayı: 1, 153 - 164, 30.03.2022
https://doi.org/10.31801/cfsuasmas.704435

Öz

The initial idea of this paper is to investigate the split complex bi-periodic Fibonacci and Lucas numbers by using SCFLN now on. We try to show some properties of SCFLN by taking into account the properties of the split complex numbers. Then, we present interesting relationships between SCFLN.

Kaynakça

  • Aydin, F. T., Hyperbolic Fibonacci sequence, Universal Journal of Mathematics and Applications, 2(2) (2019), 59-64. https://doi.org/10.32323/ujma.473514
  • Bala, A., Verma, V., Some properties of bi-variate bi-periodic Lucas polynomials, Annals of the Romanian Society for Cell Biology, 25(4) (2021), 8778-8784. https://www.annalsofrscb.ro/index.php/journal/article/view/3598.
  • Bilgici, G., Two generalizations of Lucas sequence, Applied Mathematics and Computation, 245 (2014), 526-538. https://doi.org/10.1016/j.amc.2014.07.111.
  • Catoni, F., Boccaletti, R., Cannata, R., Catoni, V., Nichelatti, E., Zampatti, P., The Mathematics of Minkowski Space-Time, Birkhauser, Basel, 2008.
  • Dikmen, C.M., Hyperbolic Jacobsthal Numbers, Asian Research Journal of Mathematics, (2019) 1-9. https://doi.org/10.9734/arjom/2019/v15i430153
  • Edson, M., Yayenie, O., A new generalization of Fibonacci sequences and extended Binet’s formula, Integers, 9(A48) (2009), 639-654. https://doi.org/10.1515/INTEG.2009.051
  • Gargoubi, H., Kossentini, S., f-algebra structure on hyperbolic numbers, Adv. Appl. Clifford Algebr., 26(4) (2016), 1211-1233. https://doi.org/10.1007/s00006-016-0644-3
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY, 2001.
  • Khadjiev, D., Goksal Y., Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space, Adv. Appl. Clifford Algebr., 26 (2016), 645-668. https://doi.org/10.1007/s00006-015-0627-9
  • Khrennikov, A., Segre, G., An Introduction to Hyperbolic Analysis, arxiv, 2005. http://arxiv.org/abs/math-ph/0507053v2.
  • Motter, A. E, Rosa, A. F., Hyperbolic calculus, Adv. Appl. Clifford Algebr., 8(1) (1998), 109-128.
  • Sobczyk, G., The hyperbolic number plane, The College Mathematics Journal, 26(4) (1995), 268-280.
  • Soykan, Y., On hyperbolic numbers with generalized Fibonacci numbers components, preprint, (2019).
  • Soykan, Y., Gocen, M., Properties of hyperbolic generalized Pell numbers, Notes on Number Theory and Discrete Mathematics, 26(4) (2020), 136-153. https://doi.org/10.7546/nntdm.2020.26.4.136-153
  • Tan, E., Leung, H.H., Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences, Advances in Difference Equations, 2020.1 (2020), 1-11. https://doi.org/10.1186/s13662-020-2507-4
  • Tasyurdu, Y., Hyperbolic Tribonacci and Tribonacci-Lucas sequences, International Journal of Mathematical Analysis, 13(12) (2019), 565-572. https://doi.org/10.12988/ijma.2019.91167
  • Verma, V., Bala, A., On properties of generalized bi-variate bi-periodic Fibonacci polynomials, International Journal of Advanced Science and Technology, 29(3) (2020), 8065-8072.
  • Yayenie, O., A note on generalized Fibonacci sequence, Applied Mathematics and Computation, 217(12) (2011), 5603-5611. https://doi.org/10.1016/j.amc.2010.12.038
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Nazmiye Yılmaz 0000-0002-7302-2281

Yayımlanma Tarihi 30 Mart 2022
Gönderilme Tarihi 16 Mart 2020
Kabul Tarihi 18 Ağustos 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 71 Sayı: 1

Kaynak Göster

APA Yılmaz, N. (2022). Split complex bi-periodic Fibonacci and Lucas numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 153-164. https://doi.org/10.31801/cfsuasmas.704435
AMA Yılmaz N. Split complex bi-periodic Fibonacci and Lucas numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Mart 2022;71(1):153-164. doi:10.31801/cfsuasmas.704435
Chicago Yılmaz, Nazmiye. “Split Complex Bi-Periodic Fibonacci and Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, sy. 1 (Mart 2022): 153-64. https://doi.org/10.31801/cfsuasmas.704435.
EndNote Yılmaz N (01 Mart 2022) Split complex bi-periodic Fibonacci and Lucas numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 153–164.
IEEE N. Yılmaz, “Split complex bi-periodic Fibonacci and Lucas numbers”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 71, sy. 1, ss. 153–164, 2022, doi: 10.31801/cfsuasmas.704435.
ISNAD Yılmaz, Nazmiye. “Split Complex Bi-Periodic Fibonacci and Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (Mart 2022), 153-164. https://doi.org/10.31801/cfsuasmas.704435.
JAMA Yılmaz N. Split complex bi-periodic Fibonacci and Lucas numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:153–164.
MLA Yılmaz, Nazmiye. “Split Complex Bi-Periodic Fibonacci and Lucas Numbers”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 71, sy. 1, 2022, ss. 153-64, doi:10.31801/cfsuasmas.704435.
Vancouver Yılmaz N. Split complex bi-periodic Fibonacci and Lucas numbers. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):153-64.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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