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2009 | 63 | 1 | 133-138
Tytuł artykułu

Remarks on best approximation in R-trees

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
63
Numer
1
Strony
133-138
Opis fizyczny
Daty
wydano
2009-01-01
online
2010-01-22
Twórcy
autor
  • Department of Mathematics, University of Iowa, Iowa City, IA 52242-1419, USA
  • Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Bibliografia
  • Fan, K., Extensions of two fixed point theorems of F. E. Browder, Math. Zeit. 112 (1969), 234-240.[Crossref]
  • Kirk, W. A., Fixed point theorems in CAT(0) spaces and R-trees, Fixed Point Theory Appl. 2004:4 (2004), 309-316.
  • Kirk, W. A., Panyanak, B., Best approximation in R-trees, Numer. Funct. Anal. Optimiz. 28 (2007), 681-690; Erratum: Numer. Funct. Anal. Optimiz. 30 (2009), 403.[Crossref]
  • Lin, T., Proximity maps, best approximations and fixed points, Approx. Theory Appl. (N. S.) 16, no. 4 (2000), 1-16.
  • Markin, J. T., Fixed points, selections and best approximation for multivalued mappings in R-trees, Nonlinear Anal. 67 (2007), 2712-2716.[WoS]
  • Piątek, B., Best approximation of coincidence points in metric trees, Ann. Univ. Mariae Curie-Skłodowska Sect. A 62 (2008), 113-121.
  • Shahzad, N., Markin, J., Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces, J. Math. Anal. Appl. 337 (2008), 1457-1464.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10062-009-0012-z
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