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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2023 Volume 113, Issue 2, Pages 295–307 (Mi mzm13886)

This article is cited in 2 papers

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

I. Yalcinkayaa, H. El-Metwallyb, D. T. Tollua, H. Ahmadc

a Necmettin Erbakan University
b Mansoura University
c Istanbul Ticaret University

Abstract: 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, $\alpha$-cut, fuzzy difference equations, boundedness, convergence.

UDC: 517

Received: 12.04.2021
Revised: 24.01.2022

DOI: 10.4213/mzm13886


 English version:
Mathematical Notes, 2023, 113:2, 292–302

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© Steklov Math. Inst. of RAS, 2024