Construction of dual-generalized complex Fibonacci and Lucas quaternions
The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (or Vajda's like), Honsberger&#...
| المؤلفون الرئيسيون: | , , |
|---|---|
| التنسيق: | مقال |
| اللغة: | English |
| منشور في: |
Vasyl Stefanyk Precarpathian National University
2022-11-01
|
| سلاسل: | Karpatsʹkì Matematičnì Publìkacìï |
| الموضوعات: | |
| الوصول للمادة أونلاين: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4706 |
| _version_ | 1827281294637137920 |
|---|---|
| author | G.Y. Şentürk N. Gürses S. Yüce |
| author_facet | G.Y. Şentürk N. Gürses S. Yüce |
| author_sort | G.Y. Şentürk |
| collection | DOAJ |
| description | The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (or Vajda's like), Honsberger's, d'Ocagne's, Cassini's and Catalan's identities are obtained. A series of matrix representations of these special quaternions is introduced. Finally, the multiplication of dual-generalized complex Fibonacci and Lucas quaternions are also expressed as their different matrix representations. |
| first_indexed | 2024-04-24T08:56:53Z |
| format | Article |
| id | doaj.art-a844f113f6444a7ea59edce88575d9f7 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:53Z |
| publishDate | 2022-11-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-a844f113f6444a7ea59edce88575d9f72024-04-16T07:12:26ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102022-11-0114240641810.15330/cmp.14.2.406-4184105Construction of dual-generalized complex Fibonacci and Lucas quaternionsG.Y. Şentürk0https://orcid.org/0000-0002-8647-1801N. Gürses1https://orcid.org/0000-0001-8407-854XS. Yüce2https://orcid.org/0000-0002-8296-6495Istanbul Gelişim University, 34310, Istanbul, TürkiyeYildiz Technical University, 34220, Istanbul, TürkiyeYildiz Technical University, 34220, Istanbul, TürkiyeThe aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (or Vajda's like), Honsberger's, d'Ocagne's, Cassini's and Catalan's identities are obtained. A series of matrix representations of these special quaternions is introduced. Finally, the multiplication of dual-generalized complex Fibonacci and Lucas quaternions are also expressed as their different matrix representations.https://journals.pnu.edu.ua/index.php/cmp/article/view/4706quaterniondual-generalized complex numberfibonacci numberlucas number |
| spellingShingle | G.Y. Şentürk N. Gürses S. Yüce Construction of dual-generalized complex Fibonacci and Lucas quaternions Karpatsʹkì Matematičnì Publìkacìï quaternion dual-generalized complex number fibonacci number lucas number |
| title | Construction of dual-generalized complex Fibonacci and Lucas quaternions |
| title_full | Construction of dual-generalized complex Fibonacci and Lucas quaternions |
| title_fullStr | Construction of dual-generalized complex Fibonacci and Lucas quaternions |
| title_full_unstemmed | Construction of dual-generalized complex Fibonacci and Lucas quaternions |
| title_short | Construction of dual-generalized complex Fibonacci and Lucas quaternions |
| title_sort | construction of dual generalized complex fibonacci and lucas quaternions |
| topic | quaternion dual-generalized complex number fibonacci number lucas number |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/4706 |
| work_keys_str_mv | AT gysenturk constructionofdualgeneralizedcomplexfibonacciandlucasquaternions AT ngurses constructionofdualgeneralizedcomplexfibonacciandlucasquaternions AT syuce constructionofdualgeneralizedcomplexfibonacciandlucasquaternions |