Abstract

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.

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Keywords

  • Surjectivity
  • metric regularity
  • multi-valued map

Mathematics Subject Classification

49J53, 47H04, 54H25

Suggested citation

M. Ivanov, N. Zlateva. “On Characterizations of Metric Regularity of Multi-Valued Maps.” Journal of Convex Analysis 27 (2020), No. 1, 381–388.

Copyright Heldermann Verlag 2020