On the solutions of two special types of Riccati difference equation via Fibonacci numbers-Reference-Cited by-同舟云学术

On the solutions of two special types of Riccati difference equation via Fibonacci numbers

Published:2013-06-18 Issue:1 Volume:2013 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Tollu Durhasan T,Yazlik Yasin,Taskara Necati

Abstract

Abstract In this study, we investigate the solutions of two special types of the Riccati difference equation x n + 1 = 1 1 + x n and y n + 1 = 1 − 1 + y n such that their solutions are associated with Fibonacci numbers. MSC: 11B39, 39A10, 39A13.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

https://link.springer.com/content/pdf/10.1186/1687-1847-2013-174.pdf

Reference19 articles.

1. Brand L: A sequence defined by a difference equation. Am. Math. Mon. 1955, 62: 489-492. 10.2307/2307362

2. Agarwal RP: Difference Equations and Inequalities. 1st edition. Dekker, New York; 1992. (2nd ed., (2000))

3. Gibbons CH, Kulenović MRS, Ladas G:On the recursive sequence "Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML" . Math. Sci. Res. Hot-Line 2000, 4: 1-11.

4. Grove EA, Kostrov Y, Ladas G, Schultz SW: Riccati difference equations with real period-2 coefficients. Commun. Appl. Nonlinear Anal. 2007, 14: 33-56.

5. Taskara N, Uslu K, Tollu DT: The periodicity and solutions of the rational difference equation with periodic coefficients. Comput. Math. Appl. 2011, 62: 1807-1813. 10.1016/j.camwa.2011.06.024

Cited by 57 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On a General Non-Linear Difference Equation of Third-Order;Turkish Journal of Mathematics and Computer Science;2024-06-30

2. On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence;Mathematica Slovaca;2024-06-01

3. Theoretical analysis of higher-order system of difference equations with generalized balancing numbers;Mathematica Slovaca;2024-06-01

4. Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients;Mathematical and Computational Applications;2024-03-31

5. Solutions and local stability of the Jacobsthal system of difference equations;AIMS Mathematics;2024