Optimal approximate fixed point results in locally convex spaces (Q1941324)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal approximate fixed point results in locally convex spaces |
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Optimal approximate fixed point results in locally convex spaces (English)
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12 March 2013
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Let \(C\) be a convex subset of a locally convex space and let \(f: C \to \overline{C}\) be a sequentially continuous map. The authors prove that, if \(f(C)\) is totally bounded, then \(f\) has an approximate fixed point net. By several counterexamples, they prove that this result is, in a sense, the best possible.
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locally convex space
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sequentially continuous map
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totally bounded set
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approximate fixed point net
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uniformly continuous map
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