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:
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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
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