A QUANTITATIVE VERSION OF A THEOREM DUE TO BORWEIN-REICH-SHAFRIR

By Ulrich Kohlenbach. 2001

62 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c1636d92723a66a14bb641e71633f33930cdb930

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

1. Laurentiu Leustean
2. Ulrich Kohlenbach
3. Paulo Oliva
4. Genaro López-Acedo
5. David Ariza-Ruiz
6. Philipp Gerhardy
7. Miroslav Bacák
8. Jeremy Avigad

In Geometry and Topology

1. Laurentiu Leustean
2. Paulo Oliva
3. Ulrich Kohlenbach
4. Genaro López-Acedo
5. David Ariza-Ruiz
6. Jeremy Avigad
7. Philipp Gerhardy
8. Miroslav Bacák

In Numerical Analysis

1. Laurentiu Leustean
2. Paulo Oliva
3. Ulrich Kohlenbach

Citations in the corpus

• Proof Mining: A Systematic Way of Analysing Proofs in Mathematics (2002, methodology): “dependence from x;x and f can be removed altogether as kx f(x)k and kx xk both can be replaced by d. Moreover, it follows that the bound only depends on d but not on C itself (see [ 57 ]).”
• Some logical metatheorems with applications in functional analysis (2003, background): “In particular, it follows from these results that a single use of sequential compactness (over a sufficiently weak base system) only gives rise to at most primitive recursive complexity in the sense of Kleene (often only simple exponential complexity) and this corresponds exactly to the complexity o”
• A quadratic rate of asymptotic regularity for CAT(0)-spaces (2005, background): “By a logical analysis of the proof of a theorem due to Borwein/Reich/Shafrir [2] (which generalizes Ishikawa’s result to unbounded C), Kohlenbach [17] obtained for the first time explicit bounds on the asymptotic regularity when general sequences (λn) satisfying (3), (4) are considered.”
• Uniform asymptotic regularity for Mann iterates (2002, methodology): “In the next section we use a result from [16] to prove a uniform bound on the convergence in theorem 1.8 thereby generalizing a corresponding result for corollary 1.4 from [16].”
• Mann iterates of directionally nonexpansive mappings in hyperbolic spaces (2002, methodology): “This paper continues the approach of applying methods from Mathematical Logic to proofs in metric fixed point theory started by the first author in [12],[13],[14].”