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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
Borsuk-Dugundji type extension theorems with Busemann convex target spaces
(Finnish Academy of Science and Letters, 2018)
In this work we study continuity properties of convex combinations in Busemann convex geodesic spaces and apply them to obtain two extension results for continuous and Lipschitz mappings with values in a Busemann convex space.
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 ...