On the first-order autonomous interval-valued difference equations under gH-difference

Document Type : Research Paper


1 Beijing Key Lab on Mathematical Characterization, Analysis, and Applications of Complex Information, School of Mathematics and Statistics, Beijing Institute of Technology, 100081, Beijing, China

2 CITMAga, 15782 Santiago de Compostela, Spain

3 Departamento de Estat\'istica, An\'alise Matem\'atica e Optimizaci\'on, Facultade de Matem\'aticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain


The theory of interval-valued difference equations under $gH$-difference is an interesting topic, since it can be applied to study numerical solutions to interval-valued or fuzzy-valued differential equations. In this paper, we estimate the number of solutions to a class of first-order interval-valued difference equations under $gH$-difference, which reveals the complexity of the stability analysis in this area, as well as the difficulty for prediction and control problems. Then, based on the relative positions of initial values and equilibrium points, we provide sufficient conditions for the existence of convergent solutions. We also provide examples to illustrate the validity of our results.


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