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

  • Toufic El Arwadi
  • Mohamed Amine Cherif


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.


Fixed-point theory Frechet topological vector space Krasnoselskii fixed-point theorems Schauder fixed-point theorems Dunford–Pettis property 

Mathematics Subject Classification

65M12 65J10 


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Copyright information

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Authors and Affiliations

  1. 1.Department of Mathematics and Computer Sciences, Faculty of ScienceBeirut Arab universityBeirutLebanon
  2. 2.Departement de Mathématiques, Faculté des Sciences de SfaxUniversité de SfaxSfaxTunisia

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