A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals
We study the convergence of the iterations in a Hilbert space , where maps into itself and is a linear projection operator. The iterations converge to the unique fixed point of , if the operator is continuous and the Lipschitz constant . If an operator satisfies these assumptions and is an orthogonal projection such that , then the operator is defined and continuous in and satisfies .
Schauder’s Conjecture (i.eėvery compact convex set in a Hausdorff topological vector space has the f.p.p.) is reduced to the search for fixed points of suitable multivalued maps in finite dimensional spaces.