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Artículo
An abstract proximal point algorithm
(Springer, 2018)
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing ...
Artículo
A note on an ergodic theorem in weakly uniformly convex geodesic spaces
(Springer, 2015-11)
Karlsson and Margulis [A. Karlsson, G. Margulis, A multiplicative ergodic theorem and nonpositively curved spaces. Commun. Math. Phys. 208 (1999), 107-123] proved in the setting of uniformly convex geodesic spaces, which ...
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
Effective results on nonlinear ergodic averages in CAT(κ) spaces
(Cambridge University Press, 2016-12)
In this paper we apply proof mining techniques to compute, in the setting of CAT(κ) spaces (with κ > 0), effective and highly uniform rates of asymptotic regularity and metastability for a nonlinear generalization of the ...
Artículo
Effective results on compositions of nonexpansive mappings
(Elsevier, 2014-02-15)
This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of (r, δ)-convex spaces, a class ...
Artículo
Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces
(Elsevier, 2013-08)
We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates. We use methods of proof mining to obtain an explicit ...