Since 2014
General Logical Metatheorems for Functional Analysis
BRICS Report Series
View Archive Info| Field | Value | |
| Title |
General Logical Metatheorems for Functional Analysis
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| Creator |
Gerhardy, Philipp
Kohlenbach, Ulrich |
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| Description |
In this paper we prove general logical metatheorems which state that for large classes of theorems and proofs in (nonlinear) functional analysis it is possible to extract from the proofs effective bounds which depend only on very sparse local bounds on certain parameters. This means that the bounds are uniform for all parameters meeting these weak local boundedness conditions. The results vastly generalize related theorems due to the second author where the global boundedness of the underlying metric space (resp. a convex subset of a normed space) was assumed. Our results treat general classes of spaces such as metric, hyperbolic, CAT(0), normed, uniformly convex and inner product spaces and classes of functions such as nonexpansive, Hölder-Lipschitz, uniformly continuous, bounded and weakly quasi-nonexpansive ones. We give several applications in the area of metric fixed point theory. In particular, we show that the uniformities observed in a number of recently found effective bounds (by proof theoretic analysis) can be seen as instances of our general logical results.
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| Publisher |
Aarhus University
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| Contributor |
—
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| Date |
2005-07-11
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| Type |
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion — |
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| Format |
application/pdf
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| Identifier |
https://tidsskrift.dk/brics/article/view/21887
10.7146/brics.v12i21.21887 |
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| Source |
BRICS Report Series; No 21 (2005): RS-21 General Logical Metatheorems for Functional Analysis
BRICS Report Series; No 21 (2005): RS-21 General Logical Metatheorems for Functional Analysis 1601-5355 0909-0878 |
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| Language |
eng
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| Relation |
https://tidsskrift.dk/brics/article/view/21887/19314
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| Rights |
Copyright (c) 2015 BRICS Report Series
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