A counter-example to some recent existence results on implicit variational inequalities

Paolo Cubiotti

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 415-418
  • ISSN: 0010-2628

Abstract

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In this note we prove that some recent results on an implicit variational inequality problem for multivalued mappings, which seem to extend and improve some well-known and celebrated results, are not correct.

How to cite

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Cubiotti, Paolo. "A counter-example to some recent existence results on implicit variational inequalities." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 415-418. <http://eudml.org/doc/247886>.

@article{Cubiotti1996,
abstract = {In this note we prove that some recent results on an implicit variational inequality problem for multivalued mappings, which seem to extend and improve some well-known and celebrated results, are not correct.},
author = {Cubiotti, Paolo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasi-variational inequalities; lower semicontinuity; partition of unity; minimax; quasi-variational inequalities; lower semicontinuity; partition of unity; minimax principle; implicit variational inequality},
language = {eng},
number = {2},
pages = {415-418},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A counter-example to some recent existence results on implicit variational inequalities},
url = {http://eudml.org/doc/247886},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Cubiotti, Paolo
TI - A counter-example to some recent existence results on implicit variational inequalities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 415
EP - 418
AB - In this note we prove that some recent results on an implicit variational inequality problem for multivalued mappings, which seem to extend and improve some well-known and celebrated results, are not correct.
LA - eng
KW - quasi-variational inequalities; lower semicontinuity; partition of unity; minimax; quasi-variational inequalities; lower semicontinuity; partition of unity; minimax principle; implicit variational inequality
UR - http://eudml.org/doc/247886
ER -

References

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  1. Fu J., Implicit variational inequalities for multivalued mappings, J. Math. Anal. Appl. 189 (1995), 801-814. (1995) Zbl0830.49006MR1312554
  2. Mosco U., Implicit variational problems and quasivariational inequalities, in Lecture Notes in Math., vol. 543, Springer-Verlag, Berlin, 1976, pp. 83-156. MR0513202
  3. Shih M.H., Tan K.K., Generalized quasi-variational inequalities in locally convex topological vector spaces, J. Math. Anal. Appl. 108 (1985), 333-343. (1985) MR0793650
  4. Aubin J.P., Frankowska H., Set-Valued Analysis, Birkhäuser, Boston, 1990. Zbl1168.49014MR1048347
  5. Cubiotti P., An existence theorem for generalized quasi-variational inequalities, Set-Valued Anal. 1 (1993), 81-87. (1993) Zbl0781.49006MR1230371

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