On the solution of linear functional equations in Hilbert space

Josef Kolomý

Displaying similar documents to “On the solution of linear functional equations in Hilbert space”

Arranging numbers on circles to reach maximum total variations.

Liao, Ying-Jie, Shieh, Min-Zheng, Tsai, Shi-Chun (2007)

The Electronic Journal of Combinatorics [electronic only]

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Some boundedness results for systems of two rational difference equations

Gabriel Lugo, Frank Palladino (2010)

Open Mathematics

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We study k th order systems of two rational difference equations $x_{n} = \frac{α + \sum_{i = 1}^{k} β_{i} x_{n - 1} + \sum_{i = 1}^{k} γ_{i} y_{n - 1}}{A + \sum_{j = 1}^{k} B_{j} x_{n - j} + \sum_{j = 1}^{k} C_{j} y_{n - j}}, y_{n} = \frac{p + \sum_{i = 1}^{k} δ_{i} x_{n - i} + \sum_{i = 1}^{k} ε_{i} y_{n - i}}{q + \sum_{j = 1}^{k} D_{j} x_{n - j} + \sum_{j = 1}^{k} E_{j} y_{n - j}} n \in ℕ$ . In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.