A smooth variational principle and more about Asplund spaces
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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:
KeywordsBanach Space Asplund Space Differentiable Norm Open Convex Subset Gateau Derivative
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