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Existence of fixed points of nonexpansive mappings in certain Banach lattices


Author: Paolo M. Soardi
Journal: Proc. Amer. Math. Soc. 73 (1979), 25-29
MSC: Primary 47H10; Secondary 46B30
DOI: https://doi.org/10.1090/S0002-9939-1979-0512051-6
MathSciNet review: 512051
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Abstract: A fixed point theorem for nonexpansive mappings in dual Banach spaces is proved. Applications in certain Banach lattices are given.


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

  • [1] W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 76 (1965), 1004-1006. MR 0189009 (32:6436)
  • [2] -, Nonexpansive mappings and the weak closure of sequences of iterates, Duke Math. J. 36 (1969), 639-645. MR 0248579 (40:1831)
  • [3] L. A. Karlovitz, On nonexpansive mappings, Proc. Amer. Math. Soc. 59 (1976), 321-325. MR 0405182 (53:8976)
  • [4] H. H. Schaefer, Banach lattices and positive operators, Springer-Verlag, Berlin and New York, 1974. MR 0423039 (54:11023)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0512051-6
Keywords: Fixed points, nonexpansive mappings, dual Banach spaces, AM-spaces, uniform relative normal structure
Article copyright: © Copyright 1979 American Mathematical Society

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