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 (zn)(zn) is a sequence of positive fuzzy numbers, AA and the initial conditions z−jz−j (j=0,1,2) (j=0,1,2) are positive fuzzy numbers and pp is a positive integer.