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Proceedings of the American Mathematical Society

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Fixed point theorems in uniformly convex Banach spaces


Author: Michael Edelstein
Journal: Proc. Amer. Math. Soc. 44 (1974), 369-374
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1974-0358451-4
MathSciNet review: 0358451
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Abstract: The notion of an asymptotic center is used to prove a number of results concerning the existence of fixed points under certain selfmappings of a closed and bounded convex subset of a uniformly convex Banach space.


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

  • [1] F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041-1044. MR 32 #4574. MR 0187120 (32:4574)
  • [2] M. Edelstein, The construction of an asymptotic center with a fixed-point property, Bull. Amer. Math. Soc. 78 (1972), 206-208. MR 45 #1005. MR 0291917 (45:1005)
  • [3] D. Göhde, Zum Prinzip der kontraktiren Abbildung, Math. Nachr. 30 (1965), 251-258. MR 32 #8129. MR 0190718 (32:8129)
  • [4] W. A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004-1006. MR 32 #6436. MR 0189009 (32:6436)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0358451-4
Keywords: Asymptotic center, fixed points, uniformly convex Banach space
Article copyright: © Copyright 1974 American Mathematical Society

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