Birkhoff-Kellogg theorems on invariant directions for multimaps (Q1811863)

Several Birkhoff-Kellogg type theorems on invariant directions for \(\mathcal{U}^{\mathcal{K}}_{\mathcal{C}}\) multifunctions in Hausdorff locally convex topolocical vector spaces and in Hausdorff topological vector spaces are proved. As consequence, Birkhoff-Kellogg type results for Kakutani multifunctions, acyclic multifunctions, O'Neill multifunctions, approximable multifunctions, and multifunctions admissible in Górniewicz' sense are deduced. Also, invariant direction results for countably condensing multifunctions are presented.