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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Derivatives of mappings with applications to nonlinear differential equations
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by Martin Schechter PDF
Trans. Amer. Math. Soc. 293 (1986), 53-69 Request permission

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.
References
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    • V. I. Averbukh and O. G. Smolyanov, The theory of differentiation in linear topological spaces, Russian Math. Surveys 22 (1967), 201-258; The various definitions of the derivative in linear topological spaces, ibid. 23 (1968), 67-112.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 293 (1986), 53-69
  • MSC: Primary 49A52; Secondary 46G05
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0814912-5
  • MathSciNet review: 814912