Construction of dual-generalized complex Fibonacci and Lucas quaternions


ŞENTÜRK G. Y., GÜRSES N., YÜCE S.

Carpathian Mathematical Publications, vol.14, no.2, pp.406-418, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.15330/cmp.14.2.406-418
  • Journal Name: Carpathian Mathematical Publications
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.406-418
  • Keywords: quaternion, dual-generalized complex number, Fibonacci number, Lucas number
  • Yıldız Technical University Affiliated: Yes

Abstract

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.