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- Title
SOLVABILITY OF A THIRD-ORDER SYSTEM OF NONLINEAR DIFFERENCE EQUATIONS VIA A GENERALIZED FIBONACCI SEQUENCE.
- Authors
HAMIOUD, HAMIDA; DEKKAR, IMANE; TOUAFEK, NOURESSADAT
- Abstract
In this paper, we solve in closed-form the following third-order system of nonlinear difference equations xn+1 = ynyn−1x pn−1/xn(any qn−2 +bnynyn−1),/ yn+1 = xnxn−1y qn−1 yn(cnx pn−2 +dnxnxn−1), p,q ∈ N,n ∈ N0 where the initial values x−i, y−i,i = 0,1,2 and the parameters (an)n∈N0,(bn)n∈N0,(cn)n∈N0, (dn)n∈N0 are non-zero real numbers. The form of the solutions of the one dimensional case of our system and a more general system defined by one to one functions are also presented.
- Subjects
NONLINEAR difference equations; FIBONACCI sequence; REAL numbers; GENERALIZATION; MATHEMATICAL formulas
- Publication
Miskolc Mathematical Notes, 2024, Vol 25, Issue 1, p271
- ISSN
1787-2405
- Publication type
Article
- DOI
10.18514/MMN.2024.4340