## Remarks on Peano-like theorems for fuzzy differential equations.(English)Zbl 0742.34058

From the author’s summary: “The validity of the classical Peano theorem is noted for differential equations on the metric space $$({\mathcal E}^ n,d_ p)$$ of normal fuzzy convex sets in $$\mathbb{R}^ n$$, where $$d_ p$$ is the $$p$$-th mean of the Hausdorff distances between corresponding level sets.”.

### MSC:

 34G99 Differential equations in abstract spaces 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 54A40 Fuzzy topology 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text:

### References:

 [1] Deimling, K., Ordinary Differential Equations in Banach Spaces, (Lecture Notes in Mathematics, 596 (1977), Springer: Springer Berlin) · Zbl 0555.60036 [2] Diamond, P.; Kloeden, P. E., Characterization of compact sets of fuzzy sets, Fuzzy Sets and Systems, 29, 341-348 (1989) · Zbl 0661.54011 [3] Diamond, P.; Kloeden, P. E., Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35, 241-250 (1990) · Zbl 0704.54006 [4] Kaleva, O., Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301-317 (1987) · Zbl 0646.34019 [5] Kaleva, O., The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35, 389-396 (1990) · Zbl 0696.34005 [6] Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319-330 (1987) · Zbl 0643.34005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.