A smooth variational principle and more about Asplund spaces

  • Robert R. Phelps
Part of the Lecture Notes in Mathematics book series (LNM, volume 1364)


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:


Banach Space Asplund Space Differentiable Norm Open Convex Subset Gateau Derivative 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Robert R. Phelps
    • 1
  1. 1.Department of Mathematics GN-50University of WashingtonSeattleUSA

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