Geodesic
On Characterizations of Metric Regularity of Multi-Valued Maps
Journal of convex analysis, Tome 27 (2020) no. 1, pp. 381-388
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We provide a new proof along the lines of the recent book of A. Ioffe [Variational Analysis of Regular Mappings: Theory and Applications, Springer Monographs in Mathematics (2017)] of a result of H. Frankowska [Some inverse mapping theorems, Ann. Inst. H. Poincaré, Anal. Non Linéaire 7 (1990) 183--234] showing that metric regularity of a multi-valued map can be characterized by regularity of its contingent variation -- a notion extending contingent derivative.
Classification : 49J53, 47H04, 54H25
Mots-clés : Surjectivity, metric regularity, multi-valued map 
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     author = {M. Ivanov and N. Zlateva},
     title = {On {Characterizations} of {Metric} {Regularity} of {Multi-Valued} {Maps}},
     journal = {Journal of convex analysis},
     pages = {381--388},
     year = {2020},
     volume = {27},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_1_JCA_2020_27_1_a21/}
}
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M. Ivanov; N. Zlateva. On Characterizations of Metric Regularity of Multi-Valued Maps. Journal of convex analysis, Tome 27 (2020) no. 1, pp. 381-388. http://geodesic.mathdoc.fr/item/JCA_2020_27_1_JCA_2020_27_1_a21/