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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuous dependence of fixed point sets
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by J. T. Markin PDF
Proc. Amer. Math. Soc. 38 (1973), 545-547 Request permission

Abstract:

The stability of the fixed point sets of a uniformly convergent sequence of set valued contractions is proved under the assumption that the maps are defined on a closed bounded subset $B$ of Hilbert space and take values in the family of nonempty closed convex subsets of $B$.
References
  • Sam B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475–488. MR 254828
  • J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
  • A. F. Filippov, Classical solutions of differential equations with multi-valued right-hand side, SIAM J. Control 5 (1967), 609–621. MR 0220995
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 38 (1973), 545-547
  • MSC: Primary 47H10
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0313897-4
  • MathSciNet review: 0313897