Fixed points and coincidences for set-valued maps. Maps of Ky Fan. (Points fixes et coincidences pour les applications multivoques (applications de Ky Fan).) (French) Zbl 0525.47042

After having introduced some classes of set-valued functions acting between topological spaces, the authors prove a continuous selection theorem, which, together with the Brouwer and Lefschetz theorem, allows them to establish some fixed point and coincidence theorems. These results include and generalize some well-known contributions of Browder and Ky Fan. In particular, also a min-max inequality of Ky Fan type can be obtained.
Reviewer: G. Caristi


47H10 Fixed-point theorems
49K35 Optimality conditions for minimax problems
54C60 Set-valued maps in general topology


Zbl 0525.47043