Ein Fixpunktsatz für mehrdeutige nichtazyklische Abbildungen auf der Sphäre. (A fixed point theorem for multivalued non-acyclic mappings on the sphere) (Q810926)

Summary: We consider the non-acyclic multi-valued mapping \(x\to T^ s(x)\) (0\(\leq s\leq n-2)\) of the (n-1)-dimensional sphere \(S^{n-1}\subset {\mathbb{R}}^ n\) on balls \(T^ s(x)=S^{n-1}\cap {\mathbb{E}}^{s+1}(x)\) and prove the existence of fixed-points \(x_ 0\in T^ s(x_ 0)\) under the condition that for arbitrary \(\phi_ 0\in T^ s(x)\) and all t with \(\| t\| \leq \delta (x)\) we can find points \(\phi_ 0+t^+_ 1\in T^ s(x+t)\) with \(\| t^+_ 1\| <\| t\|\).