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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
Mutually nearest and farthest points of sets and the Drop Theorem in geodesic spaces
(Springer, 2012-02)
Let A and X be nonempty, bounded and closed subsets of a geodesic metric space (E, d). The minimization (resp. maximization) problem denoted by min(A, X) (resp. max(A, X)) consists in finding (a0,x0)∈A×X(a0,x0)∈A×X such ...
Artículo
Geodesic Ptolemy spaces and fixed points
(Elsevier, 2011-01-01)
We prove that geodesic Ptolemy spaces with a continuous midpoint map are strictly convex. Moreover, we show that geodesic Ptolemy spaces with a uniformly continuous midpoint map are reflexive and that in such a setting ...
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
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
Continuous selections of Lipschitz extensions in metric spaces
(Springer, 2015-09)
This paper deals with the study of parameter dependence of extensions of Lipschitz mappings from the point of view of continuity. We show that if assuming appropriate curvature bounds for the spaces, the multivalued extension ...
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
Fixed points, selections and common fixed points for nonexpansive-type mappings
(Elsevier, 2011-10-15)
We study the existence of fixed points in the context of uniformly convex geodesic metric spaces, hyperconvex spaces and Banach spaces for single and multivalued mappings satisfying conditions that generalize the concept ...
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.