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

 

Derivatives of mappings with applications to nonlinear differential equations


Author: Martin Schechter
Journal: Trans. Amer. Math. Soc. 293 (1986), 53-69
MSC: Primary 49A52; Secondary 46G05
MathSciNet review: 814912
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Abstract: We present a new definition of differentiation for mappings of sets in topological vector spaces. Complete flexibility is allowed in choosing the topology with which the derivative is taken. We determine the largest space on which the derivative can act. Our definition includes all others hitherto given, and the basic theorems of calculus hold for it. Applications are considered here and elsewhere.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0814912-5
PII: S 0002-9947(1986)0814912-5
Article copyright: © Copyright 1986 American Mathematical Society