Random fixed points of 1-set contractive random maps in Fréchet spaces
This article deals with two theorems on fixed point existence for random operator \(f:\Omega \times S\to X\) \((S\) is a nonempty weakly compact convex subset of a separable Fréchet space \(X\), \((\Omega, {\mathcal A})\) a measurable space); \(f\) is either weakly inward or satisfies the Leray-Schauder condition. If \(f\) is a condensing and, for any \(\omega\in \Omega\), \(f (\omega,S)\) is bounded or if \(f\) is 1-set-contractive operator and, for any \(\omega\in \Omega\), \(f(\omega,S)\) is bounded and \(I-f(\omega, \cdot)\) is demiclosed at zero then it has a random fixed point.
scientific article; zbMATH DE number 1274771
scientific article