The Schauder and Krasnoselskii Fixed-Point Theorems on a Frechet Space

摘要

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.