Yasemin Alp and E. Gökçen Koçer

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 1, Pages 167—177

DOI: 10.7546/nntdm.2019.25.1.167-177

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## Details

### Authors and affiliations

Yasemin Alp

*Department of Mathematics-Computer Sciences, Faculty of Science
University of Necmettin Erbakan, Meram-Konya, Turkey
*

E. Gökçen Koçer

*Department of Mathematics-Computer Sciences, Faculty of Science
University of Necmettin Erbakan, Meram-Konya, Turkey
*

### Abstract

In this paper, we consider the space *R*(*p*, 1) of generalized Fibonacci sequences and orthogonal bases of this space. Using these orthogonal bases, we obtain the orthogonal projection onto a subspace *R*(*p*, 1) of ℝ^{n}. By using the orthogonal projection, we obtain the identities for the generalized Fibonacci numbers.

### Keywords

- Fibonacci numbers
- Orthogonal basis

### 2010 Mathematics Subject Classification

- 11B39
- 15A03

### References

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*ç*er, E. G. (2009). On Some Properties of Horadam Polynomials, International Mathematical Forum, 4 (25), 1243–1252. - Kalman, D., & Mena, R. (2003). The Fibonacci Numbers—Exposed, Mathematics Magazine, 76 (3), 167–181.
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## Cite this paper

APAAlp, Y. & Koçer, E. G. (2019). The identities for generalized Fibonacci numbers via orthogonal projection. Notes on Number Theory and Discrete Mathematics, 25(1), 167-177, doi: 10.7546/nntdm.2019.25.1.167-177.

ChicagoAlp, Yasemin and E. Gökçen Koçer. “The Identities for Generalized Fibonacci Numbers via Orthogonal Projection.” Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 167-177, doi: 10.7546/nntdm.2019.25.1.167-177.

MLAAlp, Yasemin and E. Gökçen Koçer. “The Identities for Generalized Fibonacci Numbers via Orthogonal Projection.” Notes on Number Theory and Discrete Mathematics 25.1 (2019): 167-177. Print, doi: 10.7546/nntdm.2019.25.1.167-177.