Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The almost fixed point property for nonexpansive mappings


Author: Simeon Reich
Journal: Proc. Amer. Math. Soc. 88 (1983), 44-46
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1983-0691276-4
MathSciNet review: 691276
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a closed convex subset of a reflexive Banach space has the almost fixed point property for nonexpansive mappings if and only if it is linearly bounded.


References [Enhancements On Off] (What's this?)

  • [1] D. E. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), 423-424. MR 612733 (82j:47070)
  • [2] J.-B. Baillon and W. O. Ray, Fixed points and approximate fixed points of nonexpansive mappings, preprint.
  • [3] K. Goebel and T. Kuczumow, A contribution to the theory of nonexpansive mappings, Bull. Calcutta Math. Soc. 70 (1978), 355-357. MR 584472 (81k:47077)
  • [4] W. A. Kirk, Fixed point theory for nonexpansive mappings, Fixed Point Theory, Lecture Notes in Math., vol. 886, Springer-Verlag, Berlin and New York, 1981, pp. 484-505. MR 643024 (83c:47076)
  • [5] E. Kohlberg and A. Neyman, Asymptotic behavior of nonexpansive mappings in normed linear spaces, Israel J. Math. 38 (1981), 269-275. MR 617673 (83g:47056)
  • [6] W. O. Ray, Nonexpansive mappings on unbounded convex domains, Bull. Acad. Polon. Sci. 26 (1978), 241-245. MR 0493551 (58:12545)
  • [7] -, The fixed point property and unbounded sets in Hilbert space, Trans. Amer. Math. Soc. 258 (1980), 531-537. MR 558189 (81e:47044)
  • [8] S. Reich, On fixed point theorems obtained from existence theorems for differential equations, J. Math. Anal. Appl. 54 (1976), 26-36. MR 0402554 (53:6373)
  • [9] -, The fixed point property for nonexpansive mappings. I, II, Amer. Math. Monthly 83 (1976), 266-268; 87 (1980), 292-294.
  • [10] -, On the asymptotic behavior of nonlinear semigroups and the range of accretive operators, J. Math. Anal. Appl. 79 (1981), 113-126. MR 603380 (82c:47066)
  • [11] -, On the asymptotic behavior of nonlinear semigroups and the range of accretive operators. II, Mathematics Research Center Report #2198, 1981; J. Math. Anal. Appl. 87 (1982), 134-146. MR 653610 (83e:47059)
  • [12] D. R. Smart, Fixed point theorems, Cambridge Univ. Press, Cambridge, 1974. MR 0467717 (57:7570)
  • [13] T. van der Walt, Fixed and almost fixed points, Mathematisch Centrum, Amsterdam, 1963. MR 0205246 (34:5079)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10

Retrieve articles in all journals with MSC: 47H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0691276-4
Keywords: Almost fixed point property, linearly bounded, nonexpansive mapping
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society