Journal of Convex Analysis 27 (2020), No. 1, 381--388
Copyright Heldermann Verlag 2020
On Characterizations of Metric Regularity of Multi-Valued Maps
Milen Ivanov
Radiant Life Technologies, Nicosia, Ciprus
milen@radiant-life-technologies.com
Nadia Zlateva
Faculty of Mathematics and Informatics, Sofia University, 1164 Sofia, Bulgaria
zlateva@fmi.uni-sofia.bg
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.
Keywords: Surjectivity, metric regularity, multi-valued map.
MSC: 49J53, 47H04, 54H25.
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