Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Chain rules for coderivatives
of multivalued mappings in Banach spaces


Authors: A. Jourani and L. Thibault
Journal: Proc. Amer. Math. Soc. 126 (1998), 1479-1485
MSC (1991): Primary 49J52, 58C20
DOI: https://doi.org/10.1090/S0002-9939-98-04198-7
MathSciNet review: 1443159
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Our basic object in this paper is to establish calculus rules for coderivatives of multivalued mappings between Banach spaces. We consider the coderivative which is associated to some geometrical approximate subdifferential for functions.


References [Enhancements On Off] (What's this?)

  • [1] J. M. Borwein and H. M. Strojwas, Tangential approximations, Nonlinear Anal. TMA, 9 (1985), 1347-1366. MR 87i:90320
  • [2] F. H. Clarke, Optimization and nonsmooth analysis, Wiley-Interscience, New York, (1983). MR 85m:49002
  • [3] A. D. Ioffe, Approximate subdifferentials and applications 1 : The finite dimensional theory, Trans. Amer. Math. Soc., 281 (1984), 389-416. MR 84m:49029
  • [4] A. D. Ioffe, Approximate subdifferentials and applications 2 : Functions on locally convex spaces, Mathematika, 33 (1986), 111-128. MR 87k:49028
  • [5] A. D. Ioffe, Approximate subdifferentials and applications 3 : Metric theory, Mathematika, 36 (1989), 1-38. MR 90g:49012
  • [6] A. Jourani, Intersection formulae and the marginal function in Banach spaces, J. Math. Anal. Appl., 192 (1995), 867-891. MR 96d:49022
  • [7] A. Jourani and L. Thibault, Verifiable conditions for openness and regularity of multivalued mappings in Banach spaces, Trans. Amer. Math. Soc., 347 (1995), 1255-1268. MR 95h:49021
  • [8] A. Jourani and L. Thibault, Extensions of subdifferential calculus rules in Banach spaces, Canadian J. Math., 48 (1996), 834-848. MR 97d:49018
  • [9] A. Jourani and L. Thibault, Coderivative of multivalued mappings, locally compact cones and metric regularity, (preprint 1995), to appear in Nonlinear Anal. Th. Meth. Appl.
  • [10] B. S. Mordukhovich, Approximation methods in problems of optimization and control, Nauka, Moscow, 1988 (in Russian; English translation to appear from Wiley-Interscience). MR 89m:49001
  • [11] B. S. Mordukhovich, On variational analysis of differential inclusions, Editors A. D. Ioffe, M. Marcus and S. Reich, Pitman Research Notes in Mathematical Series, (1990), 199-213. CMP 93:01
  • [12] B. S. Mordukhovich, Generalized differential calculus for nonsmooth and set-valued mappings, J. Math. Anal. Appl., 182 (1994), 250-288. MR 95i:49029
  • [13] B. S. Mordukhovich and Y. Shao, Nonconvex differential calculus for infinite dimensional multifunctions, Set-Valued Anal. 4 (1996), 205-236. CMP 97:02

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 49J52, 58C20

Retrieve articles in all journals with MSC (1991): 49J52, 58C20


Additional Information

A. Jourani
Affiliation: Université de Bourgogne, Laboratoire “Analyse Appliquée et Optimisation " B.P. 400, 21011 - Dijon Cédex, France
Email: jourani@satie.u-bourgogne.fr

L. Thibault
Affiliation: Université Montpellier II, Laboratoire d’Analyse Convexe, Case Courrier 05 1, 34095-Montpellier Cédex 5, France

DOI: https://doi.org/10.1090/S0002-9939-98-04198-7
Keywords: Coderivatives, approximate subdifferentials, coderivatively compactly multivalued mappings
Received by editor(s): July 7, 1995
Received by editor(s) in revised form: October 30, 1996
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society