Smooth variational principles, Asplund spaces, weak Asplund spaces

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 a key step in 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: If ƒ is lower semicontinuous on E, ε τ 0 and x 0 is such that ƒ(x0) ≤ inf E ƒ + ε, then for any λ τ 0 there exists vE such that
$$ \lambda ||x_0 - v|| \le f\left( {x_0 } \right) - f\left( v \right) \le \in and f\left( x \right) + \lambda ||x - v|| > f\left( v \right) whenever x \ne v. $$


Banach Space Maximal Monotone Operator Winning Strategy Nonempty Open Subset Bump Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

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