Leray--Schauder results for inward acyclic and approximable maps defined on Fréchet spaces (Q2371094)

Let \(E\) be a Fréchet space, \(U\) a subset of \(E\) and \(F:\overline{U}\to 2^E\) a multimap. Using the representation of \(E\) as the projective limit of a sequence of Banach spaces, the author studies the existence of fixed points of \(F\). He gives some results for Volterra, Urysohn and Kakutani--Mönch type maps satisfying the inward condition. The proofs are based on Leray--Schauder type theorems for Banach spaces.