Saleh, M.; Aloqeili, M. On the difference equation \(y_{n+1}=A + \frac {y_n}{y_{n-k}}\) with \(A < 0\). (English) Zbl 1096.39011 Appl. Math. Comput. 176, No. 1, 359-363 (2006). For the difference equation in the title the global asymptotic stability of the equilibrium \(A+1\) is studied. Reviewer: Lothar Berg (Rostock) Cited in 19 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations Keywords:recursive sequence; global asymptotic stability; rational difference equation; equilibrium PDFBibTeX XMLCite \textit{M. Saleh} and \textit{M. Aloqeili}, Appl. Math. Comput. 176, No. 1, 359--363 (2006; Zbl 1096.39011) Full Text: DOI References: [1] Abu-Saris, R.; DeVault, R., Global stability of \(y_{n + 1} = A + \frac{y_n}{y_{n - k}} \), Appl. Math. Lett., 16, 173-178 (2003) · Zbl 1049.39002 [2] Amleh, A.; Grove, E.; Ladas, G.; Georgiou, G., On the recursive sequence \(x_{n + 1} = \alpha + \frac{x_{n - 1}}{x_n} \), J. Math. Anal. Appl., 533, 790-798 (1999) · Zbl 0962.39004 [3] DeVault, R.; Schultz, S. W.; Ladas, G., On the recursive sequence \(x_{n + 1} = \frac{A}{x_n} + \frac{1}{x_{n - 2}} \), Proc. Am. Math. Soc., 126, 3257-3261 (1998) · Zbl 0904.39012 [4] DeVault, R.; Kosmala, W.; Ladas, G.; Schultz, S. W., On the recursive sequence global behavior of \(y_{n + 1} = \frac{p + y_{n - k}}{qy_n + y_{n - k}} \), Nonlinear Anal., 47, 4743-4751 (2001) · Zbl 1042.39523 [5] El-Owaidy, H.; Ahmed, A.; Mousa, M., On asymptotic behaviour of the difference equation \(x_{n + 1} = \alpha + \frac{x_{n - k}}{x_n} \), Appl. Math. Comp., 147, 163-167 (2004) · Zbl 1042.39001 [6] Kocic, V. L.; Ladas, G., Global Asymptotic Behavior of Nonlinear Difference Equations of Higher (1993), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0787.39001 [7] Kosmala, W.; Kulenovic, M. R.S.; Ladas, G.; Teixeira, C. T., On the recursive sequence \(y_{n + 1} = \frac{p + y_{n - 1}}{qy_n + y_{n - 1}} \), J. Math. Anal. Appl., 251, 571-586 (2000) · Zbl 0967.39004 [8] Kuruklis, S. A., The asymptotic stability of \(x_{n+1}\)−\( ax_n + bx_{n−k\) · Zbl 0842.39004 [9] Papanicolaou, V. G., On the asymptotic stability of a class of linear difference equations, Math. Mag., 69, 34-43 (1996) · Zbl 0866.39001 [10] M. Saleh, M. Aloqeili, On the rational difference equation \(y_{n + 1} = \frac{ A + y_{n - k}}{ y_n}\) doi:10.1016/j.amc.2005.01.094; M. Saleh, M. Aloqeili, On the rational difference equation \(y_{n + 1} = \frac{ A + y_{n - k}}{ y_n}\) doi:10.1016/j.amc.2005.01.094 · Zbl 1092.39019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.