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Documents authored by Kohlenbach, Ulrich

Document
DOI: 10.4230/DagSemProc.05021.6
Approximate fixed points of nonexpansive functions in product spaces

Authors: Ulrich Kohlenbach and Laurentiu Leustean

Published in: Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006)

Abstract
In this talk, we present another case study in the general program of proof mining in fixed point theory. Thus, we generalize results obtained by W. Kirk in the theory of approximated fixed points of nonexpansive mappings in product spaces
Cite as

Ulrich Kohlenbach and Laurentiu Leustean. Approximate fixed points of nonexpansive functions in product spaces. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{kohlenbach_et_al:DagSemProc.05021.6,
  author =	{Kohlenbach, Ulrich and Leustean, Laurentiu},
  title =	{{Approximate fixed points of nonexpansive functions in product spaces}},
  booktitle =	{Mathematics, Algorithms, Proofs},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5021},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran\c{c}oise Roy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.6},
  URN =		{urn:nbn:de:0030-drops-4330},
  doi =		{10.4230/DagSemProc.05021.6},
  annote =	{Keywords: Proof mining, fixed point theory, approximated fixed points, nonexpansive functions, product spaces}
}
Document
DOI: 10.4230/DagSemProc.05021.13
Generalized metatheorems on the extractability of uniform bounds in functional analysis

Authors: Philipp Gerhardy and Ulrich Kohlenbach

Published in: Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006)

Abstract
Recently U.Kohlenbach proved general metatheorems for the extraction of (uniform) bounds from classical proofs in functional analysis. The proof was based on a combination of Gödel's functional interpretation and Bezem's strong majorization relation. We present a generalization of the majorization relation which allows to generalize Kohlenbach's metatheorems significantly. Finally, we will discuss some examples which are now covered by the new metatheorems.
Cite as

Philipp Gerhardy and Ulrich Kohlenbach. Generalized metatheorems on the extractability of uniform bounds in functional analysis. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{gerhardy_et_al:DagSemProc.05021.13,
  author =	{Gerhardy, Philipp and Kohlenbach, Ulrich},
  title =	{{Generalized metatheorems on the extractability of uniform bounds in functional analysis}},
  booktitle =	{Mathematics, Algorithms, Proofs},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5021},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran\c{c}oise Roy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.13},
  URN =		{urn:nbn:de:0030-drops-4318},
  doi =		{10.4230/DagSemProc.05021.13},
  annote =	{Keywords: Proof mining, majorization}
}
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