Open Access

On the orbits of -closure points of ultimately nonexpansive mappings

Fixed Point Theory and Applications20062006:96737

DOI: 10.1155/FPTA/2006/96737

Received: 24 March 2006

Accepted: 12 April 2006

Published: 26 July 2006


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.


Authors’ Affiliations

Department of Mathematics and Computing Science, Saint Mary's University


  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

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