Fixed-Point Theory on a Frechet Topological Vector Space

Afif Ben Amar, Mohamed Amine Cherif and Maher Mnif

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-9

Abstract:

We establish some versions of fixed-point theorem in a Frechet topological vector space . The main result is that every map (where is a continuous map and is a continuous linear weakly compact operator) from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Krasnoselskii fixed-point theorem. Our first result extend the well-known Krasnoselskii's fixed-point theorem for U -contractions and weakly compact mappings, while the second one, by assuming that the family where and a compact is nonlinear equicontractive, we give a fixed-point theorem for the operator of the form .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:390720

DOI: 10.1155/2011/390720

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