Carpathian Mathematical Publications, vol.14, no.2, pp.406-418, 2022 (ESCI)
© Şentürk G.Y., Gürses N., Yüce S., 2022.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.