On rates of convergence in metric fixed point theory [Elektronische Ressource] / von Eyvind Martol Briseid

Description

On Rates of Convergence in MetricFixed Point TheoryVom Fachbereich Mathematikder Technischen Universitat Darmstadtzur Erlangung des Grades einesDoktors der Naturwissenschaften(Dr.rer.nat.)genehmigte DissertationvonMaster i matematikk Eyvind Martol Briseidaus Oslo, NorwegenReferent: Prof. Dr. U. Kohlenbach1. Koreferent: Prof. Dr. W.A. Kirk2.t: Prof. Dr. T. StreicherTag der Einreichung: 26. Mai 2009Tag der mundlic hen Prufung: 20. Oktober 2009Darmstadt 2009D 17iiAbstractThis thesis investigates some e ective and quantitative aspects of metric xedpoint theory in the light of methods from proof theory. The thesis consists ofcontributions to the program of proof mining, as developed by Kohlenbach andvarious collaborators since the early 1990s (but with roots back to Kreisel’s pro-gram \unwinding of proofs" from the 1950s). The contributions involve bothcase studies { studying given prima facie ine ective proofs of certain xed pointtheorems to extract \hidden" e ective information like explicit bounds and ratesof convergence for iteration sequences, and also developing further the use ofthe logical machinery involved.

Sujets

• Mathematics

Informations

• Publié par: technischen_universitat_darmstadt
• Publié le: 01 janvier 2009
• Nombre de lectures: 29
• Langue: English
• Poids de l'ouvrage: 1 Mo

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