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On a Class of Difference Equations with Interlacing Indices of the Fourth Order

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A Related Article was published on 20 February 2009

Abstract

The following class of nonlinear difference equations of the fourth order

$$ x_{n+1}=ax_{n-1}+\frac{bx_{n-1}x_{n-3}}{cx_{n-1}+dx_{n-3}},\quad n\in { \mathbb{N}}_{0}, $$

where the parameters \(a\), \(b\), \(c\), \(d\) and the initial values \(x_{-j}\), \(j=\overline{0,3}\), are positive real numbers, has been considered recently in this journal. Here we give a detailed analysis of the results and claims given therein, give many explanations and remarks related to the results and claims, explain some problems with some of the claims by providing suitable counterexamples, compare the results therein with some previous results in the literature, and present a global convergence result.

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Acknowledgements

The paper was made during the investigation supported by the Ministry of Education, Science and Technological Development of Serbia, contract no. 451-03-47/2023-01/200103.

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Authors and Affiliations

  1. Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000, Beograd, Serbia

    Stevo Stević

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China

    Stevo Stević

  3. Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000, Beograd, Serbia

    Bratislav Iričanin

  4. Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Kraljevo, Serbia

    Bratislav Iričanin

  5. Department of Mathematical Sciences, Appalachian State University, Boone, NC, 28608, USA

    Witold Kosmala

Authors
  1. Stevo Stević
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  2. Bratislav Iričanin
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  3. Witold Kosmala
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Correspondence to Stevo Stević.

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Stević, S., Iričanin, B. & Kosmala, W. On a Class of Difference Equations with Interlacing Indices of the Fourth Order. Acta Appl Math 184, 8 (2023). https://doi.org/10.1007/s10440-023-00562-w

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