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

Article

Abstract

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.

Keywords

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

© Springer International Publishing AG, part of Springer Nature 2018

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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