Journal of Prime Research in Mathematics

# On a third-order fuzzy difference equation

Ibrahim Yalcinkaya$$^{a,*}$$, Nur Atak$$^b$$, Durhasan Turgut Tollu$$^a$$
$$^a$$University, Faculty of Science, Department of Mathematics and Computer Sciences, Konya, Turkey.
$$^b$$Sarayonu Multi-Program Anatolian High School, Konya, Turkey.
Correspondence should be addressed to: Ibrahim Yalcinkaya at iyalcinkaya@erbakan.edu.tr

### Abstract

In this paper, we investigate the qualitative behavior of the fuzzy
difference equation
\begin{equation*}
z_{n+1}=\frac{z_{n-2}}{C+z_{n-2}z_{n-1}z_{n}}\
\end{equation*}
where $$n\in \mathbb{N}_{0}=\mathbb{N}\cup \left\{ 0\right\}$$, $$(z_{n})$$ is a sequence of positive fuzzy numbers, $$C$$ and initial conditions $$z_{-2},z_{-1},z_{0}$$ are positive fuzzy numbers.

#### Keywords:

Fuzzy difference equations, Existence of solutions, Boundedness, Convergence.