fixed-point theory on a frechet topological vector space
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ID: 172578
2011
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Abstract
We establish some versions of fixed-point theorem in a Frechet topological vector space E. The main result is that every map A=BC (where B is a continuous map and C 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 {T(⋅,y):y∈C(M) where M⊂E and C:M→E a compact operator} is nonlinear φ equicontractive, we give a fixed-point theorem for the operator of the form Ex:=T(x,C(x)).
| Reference Key |
amar2011internationalfixed-point
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|---|---|
| Authors | ;Afif Ben Amar;Mohamed Amine Cherif;Maher Mnif |
| Journal | structural engineering and mechanics |
| Year | 2011 |
| DOI |
10.1155/2011/390720
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| URL | |
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