3,947 research outputs found
Proof mining in metric fixed point theory and ergodic theory
In this survey we present some recent applications of proof mining to the
fixed point theory of (asymptotically) nonexpansive mappings and to the
metastability (in the sense of Terence Tao) of ergodic averages in uniformly
convex Banach spaces.Comment: appeared as OWP 2009-05, Oberwolfach Preprints; 71 page
Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings
In this paper we obtain new effective results on the Halpern iterations of
nonexpansive mappings using methods from mathematical logic or, more
specifically, proof-theoretic techniques. We give effective rates of asymptotic
regularity for the Halpern iterations of nonexpansive self-mappings of nonempty
convex sets in normed spaces. The paper presents another case study in the
project of {\em proof mining}, which is concerned with the extraction of
effective uniform bounds from (prima-facie) ineffective proofs.Comment: in C.S. Calude, G. Stefanescu, and M. Zimand (eds.), Combinatorics
and Related Areas. A Collection of Papers in Honour of the 65th Birthday of
Ioan Tomesc
- …