Advances in Difference Equations
Volume 2010 (2010), Article ID 196920, 19 pages
doi:10.1155/2010/196920
Research Article

On an Exponential-Type Fuzzy Difference Equation

G. Stefanidou, G. Papaschinopoulos, and C. J. Schinas

School of Engineering, Democritus University of Thrace, 67100 Xanthi, Greece

Received 11 March 2010; Revised 10 June 2010; Accepted 24 October 2010

Academic Editor: Roderick Melnik

Copyright © 2010 G. Stefanidou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Our goal is to investigate the existence of the positive solutions, the existence of a nonnegative equilibrium, and the convergence of a positive solution to a nonnegative equilibrium of the fuzzy difference equation 𝑥 𝑛 + 1 ∑ = ( 1 − 𝑘 − 1 𝑗 = 0 𝑥 𝑛 − 𝑗 ) ( 1 − 𝑒 − 𝐴 𝑥 𝑛 ) , 𝑘 ∈ { 2 , 3 , … } , 𝑛 = 0 , 1 , … , where 𝐴 and the initial values 𝑥 − 𝑘 + 1 , 𝑥 − 𝑘 + 2 , … , 𝑥 0 belong in a class of fuzzy numbers.