zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Existence results for systems of vector variational-like inequalities. (English) Zbl 1158.49015
Summary: The purpose of this paper is to introduce and study systems of vector variational-like inequalities in Banach spaces. Under certain conditions, some existence results for systems of vector variational-like inequalities in Banach spaces are obtained by Kakutani-Fan-Glicksberg fixed point theorem.

MSC:
49J40Variational methods including variational inequalities
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
WorldCat.org
Full Text: DOI
References:
[1] Chen, G. Y.: Existence of solutions for a vector variational inequality: an extension of hartman -- stampacchia theorem. J. optim. Theory appl. 74, 445-456 (1992) · Zbl 0795.49010
[2] Chen, Y. Q.: On the semi-monotone operation theory and application. J. math. Anal. appl. 231, 177-192 (1999) · Zbl 0934.47031
[3] Chen, G. Y.; Craven, B. D.: Approximate dual and approximate vector variational inequality for multiobjective optimization. J. aust. Math. soc. Ser. A 47, 418-423 (1989) · Zbl 0693.90089
[4] Deniilidis, A.; Hadjisavvas, N.: On the subdifferential of quasiconvex and pseudoconvex functions and cyclic monotonicity. J. math. Anal. appl. 237, 30-42 (1999) · Zbl 0934.49015
[5] Fan, K.: Some properties of convex sets related to fixed point theorems. Math. ann. 266, 519-547 (1984) · Zbl 0515.47029
[6] Fang, Y. P.; Huang, N. J.: Variational-like inequalities with generalized monotone mappings in Banach spaces. J. optim. Theory appl. 118, 327-338 (2003) · Zbl 1041.49006
[7] Fang, Y. P.; Huang, N. J.: Existence results for systems of strong implicit vector variational inequalities. Acta math. Hungar. 103, No. 4, 265-277 (2004) · Zbl 1060.49003
[8] Giannessi, F.: Theorems of alternative, quadratic programmes and complementarity problems. Variational inequalities and complementarity problems, 151-186 (1980) · Zbl 0484.90081
[9] Giannessi, F.: On minty variational principle. New trends in mathematical programming, appl. Optim. 13, 93-99 (1998) · Zbl 0909.90253
[10] F. Giannessi (Ed.), Vector Variational Inequalities and Vector Equilibria, Kluwer Academic Publishers, Dordrecht, 2000. · Zbl 0952.00009
[11] Glicksberg, I.: A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points. Proc. am. Math. soc. 3, 170-174 (1952) · Zbl 0046.12103
[12] N. Hadjisavvas, S. Schaible, Quasimonotonicity and Pseudomonotonicity in Variational Inequalities and Equilibrium Problems, Generalized Convexity, Generalized Monotonicity: Recent Results (Luminy, 1996), Nonconvex Optim. Apps. 27 (1998) 257 -- 275, Kluwer Acad. Olbl., Dordrecht. · Zbl 0946.49005
[13] Hu, J. Y.: Simultaneous vector variational inequalities and vector implicit complementarity problem. J. optim. Theory appl. 93, 141-151 (1997) · Zbl 0901.90169
[14] Hu, Sh.; Papageorgiou, N. S.: Handbook of multivalued analysis, volume I: Theory, mathematics and its applications. 419 (1997) · Zbl 0887.47001
[15] Huang, N. J.; Fang, Y. P.: Fixed point theorems and a new system of multivalued generalized order complementarity problems. Positivity 7, 257-265 (2003) · Zbl 1042.90047
[16] R. John, A note on Minty variational inequalities and generalized monotonicity, in: Generalized Convexity and Generalized Monotonicity (Karlovassi, 1999), Lecture Notes in Economics and Mathematical Systems, vol. 502, Springer, Berlin, 2001, pp. 240 -- 246. · Zbl 0977.49003
[17] Karamardian, S.; Schaible, S.: Seven kinds of monotone maps. J. optim. Theory appl. 66, 37-46 (1990) · Zbl 0679.90055
[18] Kassay, G.; Kolumbán, J.: System of multi-valued variational inequalities. Publ. math. Debrecen 56, 185-195 (2000) · Zbl 0989.49010
[19] Kassay, G.; Kolumbán, J.; Páles, Z.: Factorization of minty and stampacchia variational inequality system. Eur. J. Oper. res. 143, 377-389 (2002) · Zbl 1059.49015
[20] Konnov, I. V.: On quasimonotone variational inequalities. J. optim. Theory appl. 99, 165-181 (1998) · Zbl 0911.90325
[21] Konnov, I. V.; Yao, J. C.: On the generalized variational inequality problem. J. math. Anal. appl. 206, 42-58 (1997) · Zbl 0878.49006
[22] Lee, G. M.; Lee, B. S.; Kim, D. S.; Chen, G. Y.: On vector variational inequalities for multifunctions. Indian J. Pure appl. Math. 28, 633-939 (1997) · Zbl 0887.49005
[23] Siddiqi, A. H.; Ansari, Q. H.; Ahmad, R.: On vector variational-like inequalities. Indian J. Pure appl. Math. 26, 1135-1141 (1995) · Zbl 0856.49006
[24] Yang, X. Q.: Vector variational inequalities and vector pseudolinear optimization. J. optim. Theory appl. 95, 729-734 (1997) · Zbl 0901.90162
[25] Yang, X. Q.; Chen, G. Y.: A class of nonconvex functions and variational inequalities. J. math. Anal. appl. 169, 359-373 (1992) · Zbl 0779.90067
[26] Yang, X. Q.; Goh, C. J.: On vector variational inequality application to vector traffic equilibria. J. optim. Theory appl. 95, 431-443 (1997) · Zbl 0892.90158
[27] Yu, S. J.; Yao, J. C.: On vector variational inequalities. J. optim. Theory appl. 89, 749-769 (1996) · Zbl 0848.49012
[28] Yuan, G. X. Z.: KKM theory and applications in nonlinear analysis. (1999) · Zbl 0936.47034