During the last two decades the program of 'proof mining'emerged which uses tools from
mathematical logic (so-called proof interpretations) to systematically extract explicit …

Proceedings of the International Congress of Mathematicians (ICM 2018) : PROOF-THEORETIC
METHODS IN NONLINEAR ANALYSIS Page 1 P . I . C . M . – 2018 Rio de Janeiro, Vol. 2 (61–82) …

Accretive and monotone operator theory are central branches of nonlinear functional
analysis and constitute the abstract study of certain set-valued mappings between function …

We consider the extent to which one can compute bounds on the rate of convergence of a
sequence of ergodic averages. It is not difficult to construct an example of a computable …

We introduce constructive and classical systems for nonstandard arithmetic and show how
variants of the functional interpretations due to Gödel and Shoenfield can be used to rewrite …

This paper is another case study in the program of logically analyzing proofs to extract new
(typically effective) information ('proof mining'). We extract explicit uniform rates of …

The Digital and the Real World : Introduction Page 1 Chapter 1 Introduction Historically, the
theory of algorithms and computability started in the beginning of the last century with …

The main observation of this paper is that some sequential weak compactness arguments in
Hilbert space theory can be replaced by Heine/Borel compactness arguments (for the strong …

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in
uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel'skiı …

We provide quantitative and abstract strong convergence results for sequences from a
compact metric space satisfying a certain form of generalized Fejér monotonicity where (1) …