Por Pedro Pinto (Universidade de Lisboa, CMAF-CIO).
Abstract: In [2], Kohlenbach did an analysis of the proof of Browder's theorem (in [1]) via the monotone functional interpretation. I will be following the same outline but guided by the bounded functional interpretation ([3], [4]). Although the bounds obtained are the same, this example provides a first look at how the bounded functional interpretation works in practice.
[1] Browder, Felix E, Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces, Archive for Rational Mechanics and Analysis, vol. 24 (1967), no. 1, pp. 82-90.
[2] Kohlenbach, Ulrich, On quantitative versions of theorems due to F.E. Browder and R. Wittmann, Advances in Mathematics, vol. 226 (2011), no. 3, pp. 2764-2795.
[3] Ferreira, Fernando and Oliva, Paulo, Bounded functional interpretation, Annals of Pure and Applied Logic, vol. 135 (2005), no. 1-3, pp. 73-112.
[4] Ferreira, Fernando, Injecting uniformities into Peano arithmetic, Annals of Pure and Applied Logic, vol. 157 (2009), no. 2, pp. 122-129.
This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.
