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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nonlinear mappings in locally convex spaces


Author: Terrence S. McDermott
Journal: Trans. Amer. Math. Soc. 153 (1971), 157-165
MSC: Primary 47.80
MathSciNet review: 0270232
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0270232-0
PII: S 0002-9947(1971)0270232-0
Keywords: Bounded set, local linear approximation, open mapping, continuous inverse
Article copyright: © Copyright 1971 American Mathematical Society