Nonlinear mappings in locally convex spaces
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- by Terrence S. McDermott
- Trans. Amer. Math. Soc. 153 (1971), 157-165
- DOI: https://doi.org/10.1090/S0002-9947-1971-0270232-0
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Abstract:
A notion of local linear approximation is defined for a nonlinear mapping, $f$, defined on one locally convex linear topological space with values in another. By use of this notion, theorems on the local solvability of the equation $y = f(x)$ and on the existence of a local inverse for $f$ are obtained. The continuity and linear approximability of the inverse are discussed. In addition, a relationship between the notion of linear approximation used in the paper and the notion of Fréchet differentiability is shown in the case the intervening spaces are Banach spaces.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 153 (1971), 157-165
- MSC: Primary 47.80
- DOI: https://doi.org/10.1090/S0002-9947-1971-0270232-0
- MathSciNet review: 0270232