On a nonlinear fuzzy difference equation

Abstract

In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation

\[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\]

where $\left(z_n\right)$ is a sequence of positive fuzzy numbers, $A$ and the initial conditions $z_{-j}$ $(j=0,1,2)$are positive fuzzy numbers and $p$ is a positive integer.

Keywords

• Asymptotic behavior
• $\alpha -$cuts
• boundedness
• fuzzy difference equations
• fuzzy number
• stability

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