Hyper-dual Horadam quaternions

Abstract

This paper deals with developing a new class of quaternions, called hyper-dual Horadam quaternions which are constructed from the quaternions whose components are hyper-dual Horadam numbers. We investigate the algebraic properties of these quaternions.

On a generalization of dual-generalized complex Fibonacci quaternions

“…Some algebraic properties of these quaternions such as Vajda's identity, Catalan's identity, Cassini's identity, and d'Ocagne's identity are derived with the help of the Binet formula. Our results can be seen as a generalization of many previous works in the literature such as [1,6,15,16].…”

“…Dual-complex Fibonacci p-numbers were studied by Prasad [30]. Recently, Ait-Amrane et al [1] have introduced the hyper-dual Horadam quaternions. These numbers can also be seen as hyper-dual numbers with Horadam quaternion coefficients.…”

On unrestricted dual-generalized complex Horadam numbers

“…Specifically, Cihan et al [4] pioneered the study of dual-hyperbolic Fibonacci and Lucas numbers, while Gungor and Azak [10] established the framework for dual-complex Fibonacci and Lucas numbers. In a similar context, Tan et al [21] introduced the concept of hyperdual Horadam quaternions. Furthermore, Gurses et al [12] innovatively presented the dual-generalized complex Fibonacci quaternions, utilizing dual Fibonacci numbers as coefficients in lieu of real numbers.…”