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Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem. (English) Zbl 0795.49010

Summary: A vector variational inequality is studied. The paper deals with existence theorems for solutions under convexity assumptions and without convexity assumptions.

MSC:

49J40 Variational inequalities
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[1] Giannessi, F.,Theorems of Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, John Wiley and Sons, Chichester, England, pp. 151-186, 1980. · Zbl 0484.90081
[2] Chen, G. Y., andCheng, G. M.,Vector Variational Inequality and Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Heidelberg, Germany, Vol. 285, 1987.
[3] Chen, G. Y., andCraven, B. D.,A Vector Variational Inequality and Optimization over an Efficient Set, Zeitschrift f?r Operations Research, Vol. 3, pp. 1-12, 1990.
[4] Chen, G. Y., andYang, X. Q.,Vector Complementarity Problem and Its Equivalences with Weak Minimal Element in Ordered Space, Journal of Mathematical Analysis and Applications, Vol. 153, pp. 136-158, 1990. · Zbl 0719.90078
[5] Hartmann, G. J., andStampacchia, G.,On Some Nonlinear Elliptic Differential Functional Equations, Acta Mathematica, Vol. 115, pp. 271-310, 1966. · Zbl 0142.38102
[6] Fan, K.,A Generalization of Tychonoff’s Fixed-Point Theorem, Mathematics Annals, Vol. 142, pp. 305-310, 1961. · Zbl 0093.36701
[7] Ferrero, O.,Theorems of the Alternative for Set-valued Functions in Infinite-Dimensional Spaces, Optimization, Vol. 20, pp. 167-175, 1989. · Zbl 0676.90099
[8] Dugudji, J., andGranas, A.,KKM Maps and Variational Inequalities, Annali dell Scuola Normale Superiore, Pisa, Italy, pp. 679-682, 1979.
[9] Bardaro, C., andCappitelli, R.,Some Further Generalizations of the Knoster-Kuratowski-Mazukiewicz Theorem and Minimax Inequalities, Journal of Mathematical Analysis and Applications, Vol. 132, pp. 484-490, 1988. · Zbl 0667.49016
[10] De Luca, M., andMaugeri, A.,Quasi-Variational Inequalities and Applications to Equilibrium Problems with Elastic Demand, Nonsmooth Optimization and Related Topics, Edited by F. H. Clarke, V. F. Demyanov, and F. Giannessi, Plenum, New York, New York, pp. 61-77, 1989. · Zbl 0746.90018
[11] Holmes, R. B.,Geometric Functional Analysis and Its Applications, Springer-Verlag, Heidelberg, Germany, 1975. · Zbl 0336.46001
[12] Martein, L.,Stationary Points and Necessary Conditions in Vector Extremum Problems, Research Report No. 133, Optimization and Operations Research Group, Department of Mathematics, University of Pisa, Pisa, Italy, 1986.
[13] Jameson, G.,Ordered Linear Spaces, Springer-Verlag, Heidelberg, Germany, 1970. · Zbl 0196.13401
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