×

zbMATH — the first resource for mathematics

On the solutions of two special types of Riccati difference equation via Fibonacci numbers. (English) Zbl 1390.39020
Summary: In this study, we investigate the solutions of two special types of the Riccati difference equation \(x_{n+1}=\frac{1}{1+x_n}\) and \(y_{n+1}=\frac{1}{-1+y_n}\) such that their solutions are associated with Fibonacci numbers.

MSC:
39A10 Additive difference equations
39A13 Difference equations, scaling (\(q\)-differences)
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brand, L, A sequence defined by a difference equation , Am. Math. Mon, 62, 489-492, (1955)
[2] Agarwal RP: Difference Equations and Inequalities. 1st edition. Dekker, New York; 1992. (2nd ed., (2000)) · Zbl 0925.39001
[3] Gibbons, CH; Kulenović, MRS; Ladas, G, on the recursive sequence [inlineequation not available: see fulltext.], Math. Sci. Res. Hot-Line, 4, 1-11, (2000) · Zbl 1039.39004
[4] Grove, EA; Kostrov, Y; Ladas, G; Schultz, SW, Riccati difference equations with real period-2 coefficients , Commun. Appl. Nonlinear Anal, 14, 33-56, (2007) · Zbl 1126.39001
[5] Taskara, N; Uslu, K; Tollu, DT, the periodicity and solutions of the rational difference equation with periodic coefficients , Comput. Math. Appl, 62, 1807-1813, (2011) · Zbl 1231.39009
[6] Cinar, C, on the positive solutions of the difference equation [inlineequation not available: see fulltext.], Appl. Math. Comput, 150, 21-24, (2004) · Zbl 1050.39005
[7] Papaschinopoulos, G; Papadopoulos, BK, on the fuzzy difference equation [inlineequation not available: see fulltext.], Soft Comput, 6, 456-461, (2002) · Zbl 1033.39014
[8] Elabbasy, EM; El-Metwally, HA; Elsayed, EM, global behavior of the solutions of some difference equations, No. 2011, (2011)
[9] Elsayed, EM, solution and attractivity for a rational recursive sequence, No. 2011, (2011) · Zbl 1252.39008
[10] Elsayed, EM, on the solution of some difference equations , Eur. J. Pure Appl. Math, 4, 287-303, (2011) · Zbl 1389.39003
[11] Elsayed, EM, solutions of rational difference system of order two , Math. Comput. Model, 55, 378-384, (2012) · Zbl 1255.39003
[12] Touafek, N; Elsayed, EM, on the solutions of systems of rational difference equations , Math. Comput. Model, 55, 1987-1997, (2012) · Zbl 1255.39011
[13] Elsayed, EM, behavior and expression of the solutions of some rational difference equations , J. Comput. Anal. Appl, 15, 73-81, (2013) · Zbl 1273.39013
[14] El-Metwally, H; Elsayed, EM, solution and behavior of a third rational difference equation , Util. Math, 88, 27-42, (2012) · Zbl 1260.39011
[15] Koshy T: Fibonacci and Lucas Numbers with Applications. Wiley, New York; 2001. · Zbl 0984.11010
[16] Vajda S: Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Dover, New York; 2007.
[17] El Naschie, MS, the Golden Mean in quantum geometry, knot theory and related topics , Chaos Solitons Fractals, 10, 1303-1307, (1999) · Zbl 0959.81551
[18] Marek-Crnjac, L, on the mass spectrum of the elementary particles of the standard model using el naschie’s Golden field theory , Chaos Solitons Fractals, 15, 611-618, (2003) · Zbl 1033.81521
[19] Falcon, S; Plaza, A, the metallic ratios as limits of complex valued transformations , Chaos Solitons Fractals, 41, 1-13, (2009) · Zbl 1198.51012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.