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The Schauder and Krasnoselskii fixed-point theorems on a Frechet space. (English) Zbl 1395.65046

Summary: In this manuscript, we study some fixed-point theorems of the Schauder and Krasnoselskii type in a Frechet topological vector space \(E\). We prove a fixed-point theorem which is for every weakly compact map from a closed bounded convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has a fixed point. Using our results, we will establish a new version of the Krasnoselskii fixed-point theorem.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65J10 Numerical solutions to equations with linear operators
47H10 Fixed-point theorems
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