An Application of Proof Mining to Functional Analysis

Daniel Koernlein

Proof mining, an applied form of proof theory, has received quite some attention over the past 15 years or so. In particular, recent results by Kohlenbach and Gerhardy extract from prima facie ineffective proofs both new quantitative and qualitative information.

During the first half, this talk will introduce the work of Kohlenbach and Gerhardy suitable for application to functional analysis as well as Godel's functional ('Dialectica') interpretation, which is one of the cornerstones of proof mining. In the second, we will walk through an application to a recent asymptotic regularity result for Lipschitzian pseudocontractive mappings due to Chidume and Zegeye. This case study will reveal a qualitative strengthening of the theorem and one of its lemmas as well as a full rate of asymptotic regularity.