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On the Recursive Sequence \( {x}_{n+1}=\frac{x_{n-\left(k+1\right)}}{1+{x}_n{x}_{n-1}\dots {x}_{n-k}} \)

  • Dağıstan Simsek
  • Fahreddin G. Abdullayev
Article

Abstract

A solution of the following difference equation is investigated:
$$ {x}_{n+1}=\frac{x_{n-\left(k+1\right)}}{1+{x}_n{x}_{n-1}\dots {x}_{n-k}},n=0,1,2,\dots $$

where x(k+1); x−k; : : : ; x1; x0 𝜖 (0;∞) and k = 0; 1; 2; : : : .

Keywords

Difference equation solution of period k + 2 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Kyrgyz–Turkish Manas UniversityBishkekKyrgyzstan
  2. 2.Selcuk UniversityKonyaTurkey
  3. 3.Mersin UniversityMersinTurkey

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