Skip to content


  • Research Article
  • Open Access

On the orbits of -closure points of ultimately nonexpansive mappings

Fixed Point Theory and Applications20062006:96737

  • Received: 24 March 2006
  • Accepted: 12 April 2006
  • Published:


Let be a closed subset of a Banach space and an ultimately nonexpansive commutative semigroup of continuous selfmappings. If the -closure of is nonempty, then the closure of the orbit of any -closure point is a commutative topological group.


  • Differential Geometry
  • Computational Biology


Authors’ Affiliations

Department of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, Canada, B3H 3C3


  1. Dafermos CM, Slemrod M: Asymptotic behavior of nonlinear contraction semigroups. Journal of Functional Analysis 1973,13(1):97–106. 10.1016/0022-1236(73)90069-4MathSciNetView ArticleMATHGoogle Scholar
  2. Edelstein M: On nonexpansive mappings. Proceedings of the American Mathematical Society 1964,15(5):689–695. 10.1090/S0002-9939-1964-0165498-3MathSciNetView ArticleMATHGoogle Scholar
  3. Edelstein M, Kiang MT: On ultimately nonexpansive semigroups. Pacific Journal of Mathematics 1982,101(1):93–102.MathSciNetView ArticleMATHGoogle Scholar
  4. Edelstein M, Kiang MT: A common fixed-point theorem in reflexive locally uniformly convex Banach spaces. Proceedings of the American Mathematical Society 1985,94(3):411–415. 10.1090/S0002-9939-1985-0787883-2MathSciNetView ArticleMATHGoogle Scholar
  5. Holmes RD, Narayanaswami PP: On asymptotically nonexpansive semigroups of mappings. Canadian Mathematical Bulletin 1970, 13: 209–214. 10.4153/CMB-1970-042-1MathSciNetView ArticleMATHGoogle Scholar
  6. Khamsi MA, Lin M, Sine R: On the fixed points of commuting nonexpansive maps in hyperconvex spaces. Journal of Mathematical Analysis and Applications 1992,168(2):372–380. 10.1016/0022-247X(92)90165-AMathSciNetView ArticleMATHGoogle Scholar
  7. Roehrig SF, Sine RC: The structure of -limit sets of nonexpansive maps. Proceedings of the American Mathematical Society 1981,81(3):398–400.MathSciNetMATHGoogle Scholar


© Mo Tak Kiang. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.