Effective metastability of Halpern iterates in CAT(0) spaces
By Ulrich Kohlenbach, Laurentiu Leustean. 2011
53 citations recorded by the source corpus.
This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction of this rate from an ineffective proof due to Saejung is an instance of the general proof mining program which uses tools from mathematical logic to uncover hidden computational content from proofs. This methodology is applied here for the first time to a proof that uses Banach limits and hence makes a substantial reference to the axiom of choice.
Subfields: Computational Theory and Mathematics, Economics and Econometrics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/53624c81f26a3b436caacd5707ad61f7483cb490
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Ulrich Kohlenbach
- Laurentiu Leustean
- Paulo Oliva
- Genaro López-Acedo
- David Ariza-Ruiz
- Philipp Gerhardy
- Jeremy Avigad
In Economics and Econometrics
In Geometry and Topology
- Ulrich Kohlenbach
- Laurentiu Leustean
- Paulo Oliva
- Genaro López-Acedo
- David Ariza-Ruiz
- Jeremy Avigad
- Philipp Gerhardy
- Henry Towsner
Citations in the corpus
- PROOF-THEORETIC METHODS IN NONLINEAR ANALYSIS (2019, background): “• Since then, many papers extracting explicit rates of metastability have appeared, including [3, 36, 37, 38, 41, 44, 45, 46, 47, 50, 57, 64, 66].”