PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1998 | 156 | 1 | 67-72
Tytuł artykułu

Hyperconvexity of ℝ-trees

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
Rocznik
Tom
156
Numer
1
Strony
67-72
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-01-16
poprawiono
1997-10-14
Twórcy
autor
  • Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419, U.S.A., kirk@math.uiowa.edu
Bibliografia
  • [1] N. Aronszajn and P. Panitchpakdi, Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439.
  • [2] J. B. Baillon, Nonexpansive mappings and hyperconvex spaces, in: Fixed Point Theory and its Applications, R. F. Brown (ed.), Contemp. Math. 72, Amer. Math. Soc., Providence, R.I., 1988, 11-19.
  • [3] L. M. Blumenthal, Distance Geometry, Oxford Univ. Press, London, 1953.
  • [4] J. R. Isbell, Six theorems about injective metric spaces, Comment. Math. Helv. 39 (1964), 439-447.
  • [5] E. Jawhari, D. Misane and M. Pouzet, Retracts: graphs and ordered sets from the metric point of view, in: Combinatorics and Ordered Graphs, I. Rival (ed.), Contemp. Math. 57, Amer. Math. Soc., Providence, R.I., 1986, 175-226.
  • [6] M. A. Khamsi, On metric spaces with uniform normal structure, Proc. Amer. Math. Soc. 106 (1989), 723-726.
  • [7] M. A. Khamsi, KKM and Ky Fan theorems in hyperconvex metric spaces, J. Math. Anal. Appl. 204 (1996), 298-306.
  • [8] W. A. Kirk and S. S. Shin, Fixed point theorems in hyperconvex spaces, Houston J. Math. 23 (1997), 175-188.
  • [9] J. Kulesza and T. C. Lim, On weak compactness and countable weak compactness in fixed point theory, Proc. Amer. Math. Soc. 124 (1996), 3345-3349.
  • [10] H. E. Lacey, The Isometric Theory of Classical Banach Spaces, Springer, Berlin, 1974.
  • [11] R. Mańka, Association and fixed points, Fund. Math. 91 (1976), 105-121.
  • [12] J. W. Morgan, Λ-trees and their applications, Bull. Amer. Math. Soc. 26 (1992), 87-112.
  • [13] F. Rimlinger, Free actions on ℝ-trees, Trans. Amer. Math. Soc. 332 (1992), 313-329.
  • [14] R. Sine, On nonlinear contractions in sup norm spaces, Nonlinear Anal. 3 (1979), 885-890.
  • [15] P. Soardi, Existence of fixed points of nonexpansive mappings in certain Banach lattices, Proc. Amer. Math. Soc. 73 (1979), 25-29.
  • [16] F. Sullivan, Ordering and completeness of metric spaces, Nieuw Arch. Wisk. (3) 29 (1981), 178-193.
  • [17] J. Tits, A "Theorem of Lie-Kolchin" for trees, in: Contributions to Algebra: a Collection of Papers Dedicated to Ellis Kolchin, Academic Press, New York, 1977, 377-388.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv156i1p67bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.