Uniform asymptotic regularity for Mann iterates

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Firmly nonexpansive mappings in classes of geodesic spaces (2012, methodology): “MR2445721 (2009k:03003) [26] U. Kohlenbach and L. Leuştean, Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces, J. Eur.”
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].”
A quadratic rate of asymptotic regularity for CAT(0)-spaces (2005, methodology): “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.”
Some logical metatheorems with applications in functional analysis (2003, background): “15 and similar rates with even stronger uniformity features: it suffices to assume that there exists a point x∗ ∈ X whose iteration sequence is bounded rather than to assume that the whole space X is bounded (see [36],[37]).”
Proof Mining: A Systematic Way of Analysing Proofs in Mathematics (2002, background): “In this section we report on the results of a recent case study of proof mining carried out by the first author (see [56, 57, 59] and – together with Laurenţiu Leuştean – [60]).”