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Proceedings of the American Mathematical Society

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

 

 

An implicit function theorem without differentiability


Author: J. Warga
Journal: Proc. Amer. Math. Soc. 69 (1978), 65-69
MSC: Primary 58C15
DOI: https://doi.org/10.1090/S0002-9939-1978-0488116-3
MathSciNet review: 0488116
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Abstract: We combine a ``global'' version of the classical inverse function theorem with Schauder's fixed point theorem to investigate the existence and continuity properties of a function $ (F,x) \to \eta (F,x)$ such that $ \eta (F,x) = F(\eta (F,x),x)$.


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  • [1] C. Berge, Topological spaces, Macmillan, New York, 1963.
  • [2] J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
  • [3] Daniel H. Wagner, Survey of measurable selection theorems, SIAM J. Control Optimization 15 (1977), no. 5, 859–903. MR 0486391, https://doi.org/10.1137/0315056
  • [4] J. Warga, Optimal control of differential and functional equations, Academic Press, New York-London, 1972. MR 0372708
  • [5] Jack Warga, Derivative containers, inverse functions, and controllability, Calculus of variations and control theory (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975; dedicated to Laurence Chisholm Young on the occasion of his 70th birthday), Academic Press, New York, 1976, pp. 13–45; errata, p. 46. Math. Res. Center, Univ. Wisconsin, Publ. No. 36. MR 0427561

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0488116-3
Keywords: Implicit functions, nondifferentiable functions, fixed points, Banach spaces, measurable and continuous selections
Article copyright: © Copyright 1978 American Mathematical Society