An R-tree is a geodesic space for which there is a unique arc joining any two of its points, and this arc is a metric segment. If X is a closed convex subset of an R-tree Y, and if T: X → 2Y is a multivalued mapping, then a point z for which [...] is called a point of best approximation. It is shown here that if T is an ε-semicontinuous mapping whose values are nonempty closed convex subsets of Y, and if T has at least two distinct points of best approximation, then T must have a fixed point. We also obtain a common best approximation theorem for a commuting pair of mappings t: X → Y and T: X → 2Y where t is single-valued continuous and T is ε-semicontinuous.
@article{bwmeta1.element.doi-10_2478_v10062-009-0012-z,
author = {William Kirk and Bancha Panyanak},
title = {Remarks on best approximation in R-trees},
journal = {Annales UMCS, Mathematica},
volume = {63},
year = {2009},
pages = {133-138},
zbl = {1191.54040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0012-z}
}
William Kirk; Bancha Panyanak. Remarks on best approximation in R-trees. Annales UMCS, Mathematica, Tome 63 (2009) pp. 133-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0012-z/
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