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Artículo
Quantitative asymptotic regularity results for the composition of two mappings
(Taylor & Francis, 2016)
In this paper, we use techniques which originate from proof mining to give rates of asymptotic regularity and metastability for a sequence associated to the composition of two firmly nonexpansive mappings.
Artículo
A proof-theoretic bound extraction theorem for CAT(κ)-spaces
(Springer, 2017-06)
Starting in 2005, general logical metatheorems have been developed that guarantee the extractability of uniform effective bounds from large classes of proofs of theorems that involve abstract metric structures X. In this ...
Artículo
Quantitative results on Fejér monotone sequences
(World Scientific, 2017)
We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fej´er monotonicity where the convergence uses the compactness of the underlying ...
Artículo
A uniform betweenness property in metric spaces and its role in the quantitative analysis of the “Lion-man” game
(MSP, 2021-01-26)
We analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform betweenness property and use it in the study of a discrete ...