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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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An implicit function theorem for nondifferentiable mappings
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by Shui Nee Chow and A. Lasota PDF
Proc. Amer. Math. Soc. 34 (1972), 141-146 Request permission

Abstract:

By using Borsuk’s antipodal theorem, an implicit function theorem for nondifferentiable mappings in Banach spaces is proved. Applications of this theorem to give existence and continuous dependence on a parameter of solutions of certain boundary value problems, are shown.
References
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  • S. N. Chow, L. A. Karlovitz, and A. Lasota, An integral form of the mean value theorem for nondifferentiable mappings, J. Math. Anal. Appl. 38 (1972), 214–222. MR 305066, DOI 10.1016/0022-247X(72)90130-8
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  • A. Lasota and Z. Opial, Sur la dépendance continue des solutions des équations différentielles ordinaires de leurs seconds membres et des conditions aux limites, Ann. Polon. Math. 19 (1967), 13–36 (French). MR 208042, DOI 10.4064/ap-19-1-13-36
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 141-146
  • MSC: Primary 34A10; Secondary 46G05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0291527-7
  • MathSciNet review: 0291527