Generalized Hybrid Fibonacci and Lucas p-numbers

Abstract

The hybrid numbers are a generalization of complex, hyperbolic and dual numbers. Until this time, many researchers have studied related to hybrid numbers. In this paper, using the generalized Fibonacci and Lucas p-numbers, we introduce the generalized hybrid Fibonacci and Lucas p-numbers. Also, we give some special cases and algebraic properties of the generalized hybrid Fibonacci and Lucas p-numbers.

On Hybrid numbers with Gaussian Mersenne Coefficients

“…The authors obtain some results for the generalized On Hybrid numbers with Gaussian Mersenne Coefficients 214 tetranacci hybrid numbers, in [5]. For some similar studies, please see the references [6,7,8,9,10,11,12] and the references therein.…”

On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

“…The set of hybrid numbers forms a non-commutative ring under addition and multiplication (please see [8]). After Özdemir's paper, hybrid numbers, whose components are defined by the homogeneous recurrence relation with constant coefficients, have been studied by a large number of researchers since 2018 (please see [9][10][11][12][13][14][15]). In [16], Kızılateş and Kone introduced Fibonacci divisor hybrid numbers that generalize the Fibonacci hybrid numbers defined by Szynal-Liana and Wloch [9].…”