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Research Article | Open Access

Some properties and Vajda theorems of split dual Fibonacci and split dual Lucas octonions

Ümit Tokeşer1, Tuğba Mert2( ), Yakup Dündar1
Department of Mathematics, Faculty of Arts and Sciences, Kastamonu University, Kastamonu 37100, Turkey
Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, Sivas 58100, Turkey
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Abstract

In this paper, we introduce split dual Fibonacci and split dual Lucas octonions over the algebra O ~ ~ ( a , b , c ) , where a , b and c are real numbers. We obtain Binet formulas for these octonions. Also, we give many identities and Vajda theorems for split dual Fibonacci and split dual Lucas octonions including Catalan's identity, Cassini's identity and d'Ocagne's identity.

Keywords

octonionsdual Fibonacci and dual Lucas numberssplit dual Fibonacci and split dual Lucas octonions
CLC number: 11B39, 11R52

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8645-8653
DOI: 10.3934/math.2022483

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Cite this article:
Tokeşer Ü, Mert T, Dündar Y. Some properties and Vajda theorems of split dual Fibonacci and split dual Lucas octonions. AIMS Mathematics, 2022, 7(5): 8645-8653. https://doi.org/10.3934/math.2022483

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Received: 27 September 2021
Revised: 20 February 2022
Accepted: 22 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)