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)



Fixed points of nonexpansive mappings in Banach lattices

Authors: M. A. Khamsi and Ph. Turpin
Journal: Proc. Amer. Math. Soc. 105 (1989), 102-110
MSC: Primary 47H10; Secondary 46B30
MathSciNet review: 973841
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence of a fixed point for a nonexpansive mapping operating in a convex subset of a Banach lattice $ E$ compact for some natural topology $ \tau $ on $ E$. In particular, if $ E$ is a Banach space with a $ 1$-unconditional basis we can take for $ \tau $ the topology of coordinatewise convergence.

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

  • [A] D. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), 423-424. MR 612733 (82j:47070)
  • [B-S] J. M. Borwein and B. Sims, Non-expansive mappings on Banach lattices and related topics, Houston J. of Math. 10 (1984), 339-356. MR 763236 (86e:47059)
  • [E-L-O-S] J. Elton, P. K. Lin, E. Odell and S. Szarek, Remarks on the fixed point problem for nonexpansive maps, Contemp. Math., vol. 18, Amer. Math. Soc., Providence, R.I., 1983, pp. 87-120. MR 728595 (85d:47059)
  • [G] K. Goebel, On the structure of minimal invariant sets for nonexpansive mappings, Ann. Univ. Mariae Curie-Sklodowska 29 (1975), 73-77. MR 0461226 (57:1211)
  • [Ka] L. A. Karlovitz, Existence of fixed points of nonexpansive mappings in a space without normal structure, Pacific J. Math. 66 (1976), 153-159. MR 0435951 (55:8902)
  • [Ki1] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006. MR 0189009 (32:6436)
  • [Ki2] -, Fixed point theory for nonexpansive mappings. II, Contemp. Math., vol. 18, Amer. Math. Soc., Providence, R.I., 1983, pp. 121-140. MR 728596 (85a:47062)
  • [LD-T] E. Lami-Dozo and Ph. Turpin, Nonexpansive maps in generalized Orlicz spaces, Studia Math. 86 (1987), 155-188. MR 901907 (88h:47082)
  • [Lm] T. C. Lim, Asymptotic centers and nonexpansive mappings in conjugate Banach spaces, Pacific J. Math. 90 (1980), 135-143. MR 599326 (82h:47052)
  • [Ln] P. K. Lin, Unconditional bases and fixed points of nonexpansive mappings, Pacific J. Math. 116 (1985), 69-76. MR 769823 (86c:47075)
  • [L-T] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. II, Springer-Verlag, Berlin, Heidelberg and New York, 1979. MR 540367 (81c:46001)
  • [M] B. Maurey, Points fixes des contractions de certains faiblement compacts de $ {L^1}$, Séminaire d'Analyse Fonctionnelle 1980-81, Exposé N$ ^\circ$ VIII, Ecole Polytechnique, Palaiseau, 1981. MR 659309 (83h:47041)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10, 46B30

Retrieve articles in all journals with MSC: 47H10, 46B30

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society