Geodesic
A Variational Principle in Reflexive Spaces with Kadec-Klee Norm
Journal of convex analysis, Tome 16 (2009) no. 1, pp. 211-226.

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove a variational principle in reflexive Banach spaces X with Kadec-Klee norm, which asserts that any Lipschitz (or any proper lower semicontinuous bounded from below extended real-valued) function in X can be perturbed with a parabola in such a way that the perturbed function attains its infimum (even more can be said -- the infimum is well-posed). In addition, we have genericity of the points determining the parabolas. We prove also that the validity of such a principle actually characterizes the reflexive spaces with Kadec-Klee norm. This principle turns out to be an analytic counterpart of a result of K.-S. Lau on nearest points. 
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     author = {M. Fabian and J. Revalski},
     title = {A {Variational} {Principle} in {Reflexive} {Spaces} with {Kadec-Klee} {Norm}},
     journal = {Journal of convex analysis},
     pages = {211--226},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a10/}
}
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M. Fabian; J. Revalski. A Variational Principle in Reflexive Spaces with Kadec-Klee Norm. Journal of convex analysis, Tome 16 (2009) no. 1, pp. 211-226. http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a10/