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Monotone operators, subdifferentials and Asplund spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1364)

Abstract

A set-valued map T from a Banach space E into the subsets of its dual E* is said to be a monotone operator provided

whenever x, y c E and x* ε T(x), y* ε T(y). We do not require that T(x) be nonempty. The domain (or effective domain) D(T) of T is the set of all x ε E such that T(x) is nonempty.

Keywords

  • Banach Space
  • Monotone Operator
  • Maximal Monotone
  • Equivalent Norm
  • Maximal Monotone Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1989 Springer-Verlag Berlin Heidelberg

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Phelps, R.R. (1989). Monotone operators, subdifferentials and Asplund spaces. In: Convex Functions, Monotone Operators and Differentiability. Lecture Notes in Mathematics, vol 1364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21569-2_2

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  • DOI: https://doi.org/10.1007/978-3-662-21569-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50735-2

  • Online ISBN: 978-3-662-21569-2

  • eBook Packages: Springer Book Archive