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On the difference equation x n + 1 = a 0 x n + a 1 x n - 1 + ⋯ + a k x n - k b 0 x n + b 1 x n - 1 + ⋯ + b k x n - k

Elmetwally M. Elabbasy;  Hamdy El-Metwally;  E. M. Elsayed — 2008

Mathematica Bohemica

In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence x n + 1 = a 0 x n + a 1 x n - 1 + ⋯ + a k x n - k b 0 x n + b 1 x n - 1 + ⋯ + b k x n - k , n = 0 , 1 , ⋯ where the parameters a i and b i for i = 0 , 1 , ⋯ , k are positive real numbers and the initial conditions x - k , x - k + 1 , ⋯ , x 0 are arbitrary positive numbers.

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