Behavior of Solutions to the Fuzzy Difference Equation $z_{n+1}=A+\dfrac{B}{z_{n-m}}$

I. Yalcinkaya; H. El-Metwally; D. T. Tollu; H. Ahmad

Geodesic

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Behavior of Solutions to the Fuzzy Difference Equation $z_{n+1}=A+\dfrac{B}{z_{n-m}}$

I. Yalcinkaya ; H. El-Metwally ; D. T. Tollu ; H. Ahmad

Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 295-307

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Résumé

In this paper, we investigate the existence, the boundedness, the asymptotic behavior, and the oscillatory behavior of the positive solutions of the fuzzy difference equation $$ z_{n+1}=A+\frac{B}{z_{n-m}}\,, $$ where $n\in\mathbb{N}_{0}=\mathbb{N}\cup\{0\}$, $(z_{n})$ is a sequence of positive fuzzy numbers, $A$, $B$, and the initial conditions $z_{-j}$, $j=1, 2,\dots,m$, are positive fuzzy numbers, and $m$ is a positive integer.

Keywords: fuzzy number, fuzzy difference equations, boundedness
Mots-clés : $\alpha$-cut, convergence.

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     author = {I. Yalcinkaya and H. El-Metwally and D. T. Tollu and H. Ahmad},
     title = {Behavior of {Solutions} to the {Fuzzy} {Difference} {Equation} $z_{n+1}=A+\dfrac{B}{z_{n-m}}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {295--307},
     publisher = {mathdoc},
     volume = {113},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a11/}
}

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I. Yalcinkaya; H. El-Metwally; D. T. Tollu; H. Ahmad. Behavior of Solutions to the Fuzzy Difference Equation $z_{n+1}=A+\dfrac{B}{z_{n-m}}$. Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 295-307. http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a11/