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A smooth variational principle and more about Asplund spaces

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

Abstract

It is clear that Ekeland’s variational principle (Lemma 3.13) is an extremely useful form of the “maximality points lemma” (3.12); it was the main tool in proving Borwein’s Theorem 3.17, which in turn provided a unified approach to a sequence of fundamental results. As shown in Ekeland’s survey article [Ek], it has found application in such diverse areas as fixed-point theorems, nonlinear semigroups, optimization, mathematical programming, control theory and global analysis. Recall the statement:

Keywords

  • Banach Space
  • Asplund Space
  • Differentiable Norm
  • Open Convex Subset
  • Gateau Derivative

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). A smooth variational principle and more about 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_4

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  • DOI: https://doi.org/10.1007/978-3-662-21569-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50735-2

  • Online ISBN: 978-3-662-21569-2

  • eBook Packages: Springer Book Archive