9 citations · 25 across the 15 of their papers we have counts for
20 papers
Logical Metatheorems for Abstract Spaces axiomatized in Positive Bounded Logic II: Metric spaces and the model-theoretic uniformity principle
Ulrich Kohlenbach, Morenikeji Neri, Jin Wei
We extend the proof-theoretic treatment of uniform bound extraction from normed structures axiomatized in positive bounded logic [Advances in Mathematics, 290:503-551, 2016] (as de…
On the Computational Content of Moduli of Regularity and their Logical Strength
Ulrich Kohlenbach
We continue the investigation into the computational status of the existence of moduli of regularity (and their use for rates of convergence) in the sense of Kohlenbach, Lopez and…
Fejér monotone sequences revisited
Ulrich Kohlenbach, Pedro Pinto
In this paper we introduce a localized and relativized generalization of the usual concept of Fejér monotonicity together with uniform and quantitative versions thereof and show th…
R.E. Bruck, proof mining and a rate of asymptotic regularity for ergodic averages in Banach spaces
Anton Freund, Ulrich Kohlenbach
We analyze a proof of Bruck to obtain an explicit rate of asymptotic regularity for Cesàro means in uniformly convex Banach spaces. Our rate will only depend on a norm bound and a…
On modified Halpern and Tikhonov-Mann iterations
Horatiu Cheval, Ulrich Kohlenbach, Laurentiu Leustean
We show that the asymptotic regularity and the strong convergence of the modified Halpern iteration due to T.-H. Kim and H.-K. Xu and studied further by A. Cuntavenapit and B. Pany…
Bounds for a nonlinear ergodic theorem for Banach spaces
Anton Freund, Ulrich Kohlenbach
We extract quantitative information (specifically, a rate of metastability in the sense of Terence Tao) from a proof due to Kazuo Kobayasi and Isao Miyadera, which shows strong con…