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Proceedings of the American Mathematical Society

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

 
 

 

Continuous dependence of fixed point sets


Author: J. T. Markin
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
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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 [Enhancements On Off] (What's this?)

  • [1] S. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488. MR 40 #8035. MR 0254828 (40:8035)
  • [2] J. Dieudonné, Foundations of modern analysis, Pure and Appl. Math., vol. 10, Academic Press, New York, 1960. MR 22 #11074. MR 0120319 (22:11074)
  • [3] A. Filippov, Classical solutions of differential equations with multivalued right-hand side, SIAM J. Control 5 (1967), 609-621. MR 36 #4047. MR 0220995 (36:4047)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313897-4
Keywords: Fixed point, set valued map
Article copyright: © Copyright 1973 American Mathematical Society

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