k-ORDER FIBONACCI QUATERNIONS-Reference-Cited by-同舟云学术

k-ORDER FIBONACCI QUATERNIONS

Published:2021-03-30 Issue:1 Volume:21 Page:29-38
ISSN:2068-3049
Container-title:Journal of Science and Arts
language:en
Short-container-title:J. Sci. Arts

Author:

ASCI MUSTAFA¹,AYDINYUZ SULEYMAN¹

Affiliation:

1. Pamukkale University, Science and Arts Faculty, Department of Mathematics, 20160 Denizli, Turkey.

Abstract

In this paper, we define and study another interesting generalization of the Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for Fibonacci quaternions, for Tribonacci quaternions and for Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also, we identify and prove the matrix representation for k-order Fibonacci quaternions. The matrix given for k-order Fibonacci numbers is defined for k-order Fibonacci quaternions and after the matrices with the k-order Fibonacci quaternions is obtained with help of auxiliary matrices, important relationships and identities are established.

Publisher

Valahia University of Targoviste - Journal of Science and Arts

Reference26 articles.

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