Geodesic
Variational Methods in Classical Open Mapping Theorems
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 477-488
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We describe some basic facts from the theory of linear error bounds for lower semicontinuous functions on complete metric spaces, relying upon Ekeland's variational principle and on the notion of strong slope. We then show how this variational method yields the classical Banach-Schauder and Lusternik-Graves open mapping theorems. 
@article{JCA_2006_13_3_JCA_2006_13_3_a1,
     author = {D. Az\'e and J.-N. Corvellec},
     title = {Variational {Methods} in {Classical} {Open} {Mapping} {Theorems}},
     journal = {Journal of convex analysis},
     pages = {477--488},
     year = {2006},
     volume = {13},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a1/}
}
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D. Azé; J.-N. Corvellec. Variational Methods in Classical Open Mapping Theorems. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 477-488. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a1/