On the Solutions of Quaternion Difference Equations in Terms of Generalized Fibonacci-Type Numbers

Autor:	Kübra Gül
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	quaternion difference equation solution of difference equation recurrence sequence Mathematics QA1-939
Zdroj:	Symmetry, Vol 14, Iss 10, p 2190 (2022)
Druh dokumentu:	article
ISSN:	2073-8994
DOI:	10.3390/sym14102190
Popis:	The aim of this paper is to investigate the solution of the following difference equation zn+1=(pn)−1,n∈N0,N0=N∪0 where pn=a+bzn+czn−1zn with the parameters a, b, c and the initial values z−1,z0 are nonzero quaternions such that their solutions are associated with generalized Fibonacci-type numbers. Furthermore, we deal with the solutions to the following symmetric system of difference equations given by zn+1=(qn)−1,wn+1=(rn)−1,n∈N0 where qn=a+bwn+czn−1wn and rn=a+bzn+cwn−1zn. We provide the solution to the third-order quaternion linear difference equation in terms of the zeros of the characteristic polynomial associated with the linear difference equation.
Databáze:	Directory of Open Access Journals
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