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 generalized vector variational inequality problem. (English) Zbl 0878.49006
This paper studies vector variational inequalities with set-valued mappings. Existence results are established by applying Fan’s lemma also known as KKM theorem. A generalized vector complementarity problem is also introduced.

49J40Variational methods including variational inequalities
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
Full Text: DOI
[1] Giannessi, F.: Theory of alternative, quadratic programs and complementarity problems. Variational inequalities and complementarity problems, 151-186 (1980) · Zbl 0484.90081
[2] Chen, G. Y.; Yang, X. Q.: Vector complementarity problem and its equivalences with weak minimal element in ordered spaces. J. math. Anal. appl. 153, 136-158 (1990) · Zbl 0712.90083
[3] Chen, G. Y.; Cheng, G. M.: Vector variational inequality and vector optimization. Lecture notes in economics and mathematical systems 258, 408-416 (1987)
[4] Chen, G. Y.; Craven, B. D.: A vector variational inequality and optimization over an efficient set. Z. oper. Res. 3, 1-12 (1990) · Zbl 0693.90091
[5] Chen, G. Y.: Existence of solution for a vector variational inequality: an extension of the Hartmann-stampacchia theorem. J. optim. Theory appl. 74, 445-456 (1992) · Zbl 0795.49010
[6] Yang, X. Q.: Vector variational inequality and its duality. Nonlinear anal. 21, 869-877 (1993) · Zbl 0809.49009
[7] Yu, S. J.; Yao, J. C.: On vector variational inequalities. J. optim. Theory appl. 89, 749-769 (1996) · Zbl 0848.49012
[8] Lin, K. L.; Yang, D. P.; Yao, J. C.: Generalized vector variational inequalities. J. optim. Theory appl. 92 (1997) · Zbl 0886.90157
[9] Fang, S. C.; Petersen, E. L.: Generalized variational inequalities. J. optim. Theory appl. 38, 363-383 (1982) · Zbl 0471.49007
[10] Fan, K.: A generalization of tychonoff’s fixed-point theorem. Math. ann. 142, 305-310 (1961) · Zbl 0093.36701
[11] Knaster, B.; Kuratowski, C.; Mazurkiewicz, S.: Ein beweis des fixpunktsatzes für N dimensionale simplexe. Fund. math. 14, 132-137 (1929) · Zbl 55.0972.01
[12] Karamadian, S.: Complementarity over cones with monotone and pseudomonotone maps. J. optim. Theory appl. 18, 445-454 (1976)
[13] Minty, G.: Monotone (nonlinear) operators in Hilbert space. Duke math. J. 29, 341-346 (1962) · Zbl 0111.31202
[14] Conway, J. B.: A course in functional analysis. (1990) · Zbl 0706.46003
[15] Yao, J. C.: Multi-valued variational inequalities with K-pseudomonotone operators. J. optim. Theory appl. 83, 391-403 (1994) · Zbl 0812.47055
[16] A. Daniilidis, N. Hadjisavvas, Variational inequalities with quasimonotone multivalued operators · Zbl 0937.49003
[17] Kneser, H.: Sur le théorème fondamentale de al théorie des jeux. C. R. Acad. sci. Paris 234, 2418-2420 (1952) · Zbl 0046.12201
[18] Konnov, I. V.: Combined relaxation methods for finding equilibrium points and solving related problems. Izv. vyssh. Uchebn. zaved. Mat. 37, 44-51 (1993) · Zbl 0835.90123
[19] Konnov, I. V.: On combined relaxation methods’ convergence rates. Izv. vyssh. Uchebn. zaved. Mat. 37, 89-92 (1993) · Zbl 0842.90108