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$k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS

Yıl 2017, Cilt: 5 Sayı: 2, 102 - 113, 15.10.2017

GÖKSAL Bilgici ÜMİT Tokaşer ZAFER Ünal

Öz

We investigate the properties of $k-$Fibonacci and $k-$Lucas quaternions over the generalized quaternion algebra. After presenting generating functions and Binet's formulas for these types of quaternions, we calculate several well-known identities such as Catalan's, Cassini's and d'Ocagne's identities for $k-$Fibonacci and $k-$Lucas generalized quaternions.

Anahtar Kelimeler

$k$-Fibonacci number $k$-Lucas number generalized quaternion

Kaynakça

  • [1] Akyigit, M., Kosal, H.H. and Tosun, M., Split Fibonacci Quaternions, Adv. Appl. Clifford Algebr. Vol:23 (2014), 535-545.
  • [2] Akyigit, M., Kosal, H.H. and Tosun, M., Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebr. Vol:24 (2014), 631-641.
  • [3] Cimen, C.B. and Ipek, A., On Pell Quaternions and Pell-Lucas Quaternions, Adv. Appl. Clifford Algebr., Vol:26 (2016), 39-51.
  • [4] Catarino, P., The Modi ed Pell and the Modi ed k-Pell Quaternions and Octonions, Adv. Appl. Clifford Algebr., Vol:26 (2016), 577-590.
  • [5] Catarino, P. and Vasco, P., On Dual k􀀀Pell Quaternions and Octonions, Mediterr. J. Math., Vol:14 (2017), 75-87.
  • [6] Falcon, S. and Plaza, A., The k-Fibonacci Sequence and the Pascal 2-Triangle, Chaos Solitons Fractals, Vol:33, No.1 (2007), 38-49.
  • [7] Falcon, S., On the k-Lucas Numbers, Int. J. Contemp. Math. Sci. Vol:21 (2011), 1039-1050.
  • [8] Halici, S., On Fibonacci Quaternions, Adv. Appl. Clifford Algebr. Vol:22 (2012), 321-327.
  • [9] Harman, C.J., Complex Fibonacci Numbers, Fibonacci Quart. Vol:19, No.1 (1981), 82-86. [10] Horadam, A. F. , Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly No:70 (1963), 289-291.
  • [11] Iyer, M. R., Some Result on Fibonacci Quaternions, Fibonacci Quart. Vol:7, No.2 (1969), 201-210.
  • [12] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, 2001.
  • [13] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer-Verlag New York, USA, 2014.
  • [14] Polatli,E., Kizilates, C. and Kesim, S., On Split k􀀀Fibonacci and k-Lucas Quaternions, Adv. Appl. Clifford Algebr. Vol:26 (2016), 353-362.
  • [15] Polatli, E. and Kesim, S., A Note on Catalan's Identity for the k􀀀 Fibonacci Quaternions, J. Integer Seq. Vol:18 (Article 15.8.2 ) (2015), 1-4.
  • [16] Ramirez, J. L., Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. St. Univ. Ovidius Constanta Ser. Mat. Vol:23 No.2 (2015), 201-212.
  • [17] Tokeser, U., Unal, Z. and Bilgici, G., Split Pell and Split Pell-Lucas Quaternions, Adv. Appl. Clifford Algebr. Vol: 27 (2017), 1881-1893.
  • [18] Szynal-Liana, A. and Wloch, I. The Pell Quaternions and the Pell Octonions, Adv. Appl. Clifford Algebr. Vol:26 (2016), 435-440.

Yıl 2017, Cilt: 5 Sayı: 2, 102 - 113, 15.10.2017

GÖKSAL Bilgici ÜMİT Tokaşer ZAFER Ünal

Öz

Kaynakça

  • [1] Akyigit, M., Kosal, H.H. and Tosun, M., Split Fibonacci Quaternions, Adv. Appl. Clifford Algebr. Vol:23 (2014), 535-545.
  • [2] Akyigit, M., Kosal, H.H. and Tosun, M., Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebr. Vol:24 (2014), 631-641.
  • [3] Cimen, C.B. and Ipek, A., On Pell Quaternions and Pell-Lucas Quaternions, Adv. Appl. Clifford Algebr., Vol:26 (2016), 39-51.
  • [4] Catarino, P., The Modi ed Pell and the Modi ed k-Pell Quaternions and Octonions, Adv. Appl. Clifford Algebr., Vol:26 (2016), 577-590.
  • [5] Catarino, P. and Vasco, P., On Dual k􀀀Pell Quaternions and Octonions, Mediterr. J. Math., Vol:14 (2017), 75-87.
  • [6] Falcon, S. and Plaza, A., The k-Fibonacci Sequence and the Pascal 2-Triangle, Chaos Solitons Fractals, Vol:33, No.1 (2007), 38-49.
  • [7] Falcon, S., On the k-Lucas Numbers, Int. J. Contemp. Math. Sci. Vol:21 (2011), 1039-1050.
  • [8] Halici, S., On Fibonacci Quaternions, Adv. Appl. Clifford Algebr. Vol:22 (2012), 321-327.
  • [9] Harman, C.J., Complex Fibonacci Numbers, Fibonacci Quart. Vol:19, No.1 (1981), 82-86. [10] Horadam, A. F. , Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly No:70 (1963), 289-291.
  • [11] Iyer, M. R., Some Result on Fibonacci Quaternions, Fibonacci Quart. Vol:7, No.2 (1969), 201-210.
  • [12] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, 2001.
  • [13] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer-Verlag New York, USA, 2014.
  • [14] Polatli,E., Kizilates, C. and Kesim, S., On Split k􀀀Fibonacci and k-Lucas Quaternions, Adv. Appl. Clifford Algebr. Vol:26 (2016), 353-362.
  • [15] Polatli, E. and Kesim, S., A Note on Catalan's Identity for the k􀀀 Fibonacci Quaternions, J. Integer Seq. Vol:18 (Article 15.8.2 ) (2015), 1-4.
  • [16] Ramirez, J. L., Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. St. Univ. Ovidius Constanta Ser. Mat. Vol:23 No.2 (2015), 201-212.
  • [17] Tokeser, U., Unal, Z. and Bilgici, G., Split Pell and Split Pell-Lucas Quaternions, Adv. Appl. Clifford Algebr. Vol: 27 (2017), 1881-1893.
  • [18] Szynal-Liana, A. and Wloch, I. The Pell Quaternions and the Pell Octonions, Adv. Appl. Clifford Algebr. Vol:26 (2016), 435-440.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Articles
Yazarlar

GÖKSAL Bilgici

ÜMİT Tokaşer Bu kişi benim

ZAFER Ünal

Yayımlanma Tarihi 15 Ekim 2017
Gönderilme Tarihi 15 Ekim 2017
Kabul Tarihi 7 Haziran 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA Bilgici, G., Tokaşer, Ü., & Ünal, Z. (2017). $k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS. Konuralp Journal of Mathematics, 5(2), 102-113.
AMA Bilgici G, Tokaşer Ü, Ünal Z. $k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS. Konuralp J. Math. Ekim 2017;5(2):102-113.
Chicago Bilgici, GÖKSAL, ÜMİT Tokaşer, ve ZAFER Ünal. “$k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS”. Konuralp Journal of Mathematics 5, sy. 2 (Ekim 2017): 102-13.
EndNote Bilgici G, Tokaşer Ü, Ünal Z (01 Ekim 2017) $k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS. Konuralp Journal of Mathematics 5 2 102–113.
IEEE G. Bilgici, Ü. Tokaşer, ve Z. Ünal, “$k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS”, Konuralp J. Math., c. 5, sy. 2, ss. 102–113, 2017.
ISNAD Bilgici, GÖKSAL vd. “$k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS”. Konuralp Journal of Mathematics 5/2 (Ekim 2017), 102-113.
JAMA Bilgici G, Tokaşer Ü, Ünal Z. $k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS. Konuralp J. Math. 2017;5:102–113.
MLA Bilgici, GÖKSAL vd. “$k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS”. Konuralp Journal of Mathematics, c. 5, sy. 2, 2017, ss. 102-13.
Vancouver Bilgici G, Tokaşer Ü, Ünal Z. $k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS. Konuralp J. Math. 2017;5(2):102-13.
 Kapak Resmi İndir
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