Displaying similar documents to “On the rational recursive sequence x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i ”

On the rational recursive sequence x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k

E. M. E. Zayed, M. A. El-Moneam (2010)

Mathematica Bohemica

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The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k , n = 0 , 1 , 2 , ⋯ where the coefficients α i , β i ∈ ( 0 , ∞ ) for i = 0 , 1 , 2 , and l , k are positive integers. The initial conditions x - k , ⋯ , x - l , ⋯ , x - 1 , x 0 are arbitrary positive real numbers such that l < k . Some numerical experiments are presented.

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

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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.