Abstract
In this paper, we study the periodicity, the boundedness and the convergence of the following max-type difference equation
where \(\{A_{n}\}^{+\infty}_{n=0}\) is a periodic sequence with period k and A n ∈(0,1) for every n≥0, m∈{1,2} and r∈{2,3,…} with m<r, the initial values x −r ,…,x −1∈(0,+∞). The special case when \(m = 1, r = 2, \{A_{n}\}^{+\infty}_{ n=0}\) is a periodic sequence with period k and A n ∈(0,1) for every n≥0 has been completely investigated by Y. Chen. Here we extend his results to the general case.
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Project Supported by NSF of China (10861002) and NSF of Guangxi (2010GXNSFA013106, 2011GXNSFA014781) and SF of Education Department of Guangxi (200911MS212).
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Sun, T., Xi, H., Han, C. et al. Dynamics of the max-type difference equation \(x_{n}=\max\{\frac{ 1}{ x_{n-m}} , \frac{A_{n} }{x_{n-r} }\}\) . J. Appl. Math. Comput. 38, 173–180 (2012). https://doi.org/10.1007/s12190-010-0471-y
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DOI: https://doi.org/10.1007/s12190-010-0471-y