Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences

By S. Stević. 2014

97 citations recorded by the source corpus.

Well-defined solutions of the bilinear difference equation are represented in terms of generalized Fibonacci sequences and the initial value. Our results extend and give natural explanations of some recent results in the literature. Some applications concerning a two-dimensional system of bilinear difference equations are also given.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/843e85647717c1a7e0eb4a2a43bd0c303f7d7f3a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Yacine Halim
2. Mustafa Bayram
3. Bratislav Iricanin
4. Zdenek Smarda
5. S. Stević
6. Flavia Colonna

In Discrete Mathematics and Combinatorics

1. Yacine Halim
2. Mustafa Bayram
3. Bratislav Iricanin
4. Zdenek Smarda
5. S. Stević

In Statistical and Nonlinear Physics

1. Bratislav Iricanin
2. Zdenek Smarda
3. Witold Kosmala
4. S. Stević
5. Yacine Halim
6. Mustafa Bayram

Citations in the corpus

• Note on the bilinear difference equation with a delay (2018, background): “A traditional way for solving the equation is transforming it by a change of variables to an equation of the form in (1).”
• On the solutions of a higher‐order difference equation in terms of generalized Fibonacci sequences (2016, background): “In paper [15], Stevic gave a theoretical explanation for the formula of solutions of the following difference equation xnC1 D ̨xn C ˇ xn C ı where parameters ̨,ˇ, , and ı and the initial value x0 are real numbers.”