Fixed-Point Theory on a Frechet Topological Vector Space
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-Pe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/390720 |
| Summary: | 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)). |
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| ISSN: | 0161-1712 1687-0425 |