Construction of dual-generalized complex Fibonacci and Lucas quaternions

ŞENTÜRK G. Y., GÜRSES N., YÜCE S.

Carpathian Mathematical Publications, cilt.14, sa.2, ss.406-418, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15330/cmp.14.2.406-418
  • Dergi Adı: Carpathian Mathematical Publications
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.406-418
  • Anahtar Kelimeler: quaternion, dual-generalized complex number, Fibonacci number, Lucas number
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet’s formulas, Tagiuri’s (or Vajda’s like), Honsberger’s, d’Ocagne’s, Cassini’s and Catalan’s identities are obtained. A series of matrix representations of these special quaternions is introduced. Finally, the multiplication of dual-generalized complex Fibonacci and Lucas quaternions are also expressed as their different matrix representations.