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Weak convergence to the fixed point of an asymptotically nonexpansive map


Author: S. C. Bose
Journal: Proc. Amer. Math. Soc. 68 (1978), 305-308
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1978-0493543-4
MathSciNet review: 0493543
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Abstract: It is proved that, in certain Banach spaces, any asymptotically nonexpansive and asymptotically regular map has the property that its iterates, applied to any point in the domain, give a sequence converging weakly to a fixed point.


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

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  • [7] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. MR 0211301 (35:2183)
  • [8] -, Lecture notes on nonexpansive and monotone mappings in Banach spaces, Center for Dynamical Systems, Brown University, Providence, R. I., 1967.
  • [9] H. Schaefer, Uber die Methode sukzessiver Approximationen, Jber. Deutsch. Math.-Verein. 59 (1957), 131-140. MR 0084116 (18:811g)

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DOI: https://doi.org/10.1090/S0002-9939-1978-0493543-4
Article copyright: © Copyright 1978 American Mathematical Society

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