A note on fixed points for fuzzy mappings (Q1058126)

The following theorem was proved in [\textit{D. Butnariu}, Fuzzy Sets Syst. 7, 191-207 (1982; Zbl 0473.90087)]. Theorem. Let C be a nonempty convex compact subset of a real locally convex topological vector space. If F is a closed fuzzy mapping over C then F has a fixed point in C. In the cited paper there is no explicit mention of the normality of F(x) for all \(x\in C^ 1\). However, an example is given which shows, that this assumption cannot be omitted.