zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the existence of solutions to generalized vector variational-like inequalities. (English) Zbl 1134.49006
The authors derive a Minty type lemma for a class of generalized vector variational-like inequalities with set-valued mappings. By means of the Minty type lemma, they also prove some existence results for two classes of vector variational-like inequalities. Their approach is based on the known KKM technique.

49J40Variational methods including variational inequalities
Full Text: DOI
[1] Baiacchi, C.; Capelo, A.: Variational and quasi-variational inequalities, applications to free boundary problems. (1984)
[2] Chen, G. Y.: Existence of solution for a vector variational inequality: an extension of the hartman -- stampacchia theorem. J. optim. Theory appl. 74, No. 3, 445-456 (1992) · Zbl 0795.49010
[3] Chen, G. Y.; Yang, X. Q.: The vector complementarity problem and its equivalence with the weak minimal element in ordered sets. J. math. Anal. appl. 153, 136-158 (1990) · Zbl 0712.90083
[4] Fan, K.: A generalization of tychonoff’s fixed point theorem. Math. ann. 142, 305-310 (1961) · Zbl 0093.36701
[5] Giannessi, F.: Theorems of alternative, quadratic programmes and complementarity problems. Variational inequalities and complementarity problems, 151-186 (1980) · Zbl 0484.90081
[6] Giannessi, F.: On connections among separation, penalization and regularization for variational inequalities with point-to-set-operators. Rend. circ. Mat. Palermo ser. 2, No. Suppl. 48, 11-18 (1997)
[7] Giannessi, F.: On minty variational principle. New trends in mathematical programming (1997)
[8] Khan, M. F.; Salahuddin: On generalized vector variational-like inequalities. Nonlinear anal. 59, 879-889 (2004) · Zbl 1083.49008
[9] Kinderlehrer, D.; Stampacchia, G.: An introduction to variational inequalities. (1980) · Zbl 0457.35001
[10] Kumari, A.; Mukherjee, R. N.: On some generalized multi-valued variational inequalities. Indian J. Pure appl. Math. 31, No. 6, 667-674 (2000) · Zbl 0959.49013
[11] Lee, G. M.; Kim, D. S.; Kuk, H.: Existence of solutions for vector optimization problems. J. math. Anal. appl. 220, 90-98 (1998) · Zbl 0911.90290
[12] Lee, G. M.; Kim, D. S.; Lee, B. S.; Cho, S. J.: On vector variational inequality. Bull. korean math. Soc. 33, No. 4, 553-564 (1996) · Zbl 0871.49011
[13] Lee, B. S.; Lee, G. M.: A vector version of minty’s lemma and application. Appl. math. Lett. 12, 43-50 (1999) · Zbl 0941.49007
[14] Lee, B. S.; Lee, G. M.; Kim, D. S.: Generalized vector variational-like inequalities on locally convex Hausdorff topological vector spaces. Indian J. Pure appl. Math. 28, No. 1, 33-41 (1997) · Zbl 0899.49005
[15] Jr., S. B. Nadler: Multi-valued contraction mappings. Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002
[16] Siddiqi, A. H.; Khan, M. F.; Salahuddin: On vector variational-like inequalities. Far east J. Math. sci. Special 3, 319-329 (1998) · Zbl 1114.49300
[17] Yu, S. J.; Yao, J. C.: On vector variational inequalities. J. optim. Theory appl. 89, 749-769 (1996) · Zbl 0848.49012