The approximate fixed point property in Hausdorff topological vector spaces and applications

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July 2009, 25(2): 467-479. doi: 10.3934/dcds.2009.25.467

The approximate fixed point property in Hausdorff topological vector spaces and applications

1.	Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, 60455-760, CE, Brazil

Received October 2008 Revised February 2009 Published June 2009

Abstract
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Let l be a compact convex subset of a Hausdorff topological vector space $(\mathcal{E},\tau)$ and $\sigma$ another Hausdorff vector topology in $\mathcal{E}$. We establish an approximate fixed point result for sequentially continuous maps f: (l,$\sigma$)$\to$ (l,$\tau$). As application, we obtain the weak-approximate fixed point property for demicontinuous self-mapping weakly compact convex sets in general Banach spaces and use this to prove new results in asymptotic fixed point theory. These results are also applied to study the existence of limiting-weak solutions for differential equations in reflexive Banach spaces.

Keywords: Differential equations, Approximate fixed point property, Reflexive spaces., Asymptotic fixed point theorem, Hausdorff topological vector spaces.

Mathematics Subject Classification: Primary: 46H03; Secondary: 47H1.

Citation: Cleon S. Barroso. The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 467-479. doi: 10.3934/dcds.2009.25.467

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