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 ( z n ) (zn) is a sequence of positive fuzzy numbers, A A and the initial conditions z − j z−j ( j = 0 , 1 , 2 ) (j=0,1,2) are positive fuzzy numbers and p p is a positive integer.
Highlights
Over the last two decades, a lot of study has been published on difference equations and systems
In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation zn+1 =
We will study the existence of the positive solutions of equation (8)
Summary
Over the last two decades, a lot of study has been published on difference equations and systems One reason for this is that such equations and systems have high applicability both in mathematics and other sciences such as population biology, economics, probability theory, genetics, psychology etc., (see, e.g., [2, 6, 14, 15] and the references therein). Measurements or data on a problem may reveal uncertainty or the problem considered may require subjective interpretations In such cases, a fuzzy difference equation model can be established using notion of fuzzy set. In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation zn+1 =.
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