The penalty method for a new system of generalized variational inequalities.

Tang, Yu-Chao; Liu, Li-Wei

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Petrot, Narin (2010)

Abstract and Applied Analysis

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Coupled coincidence point theorems for nonlinear contractions in partially ordered quasi-metric spaces with a $Q$ -function.

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On the system of rational difference equations $x_{n + 1} = f (y_{n - q}, x_{n - s})$ , $y_{n + 1} = g (x_{n - t}, y_{n - p})$ .

Sun, Taixiang, Xi, Hongjian (2006)

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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.