×

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.

MSC:

49J40 Variational inequalities
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Baiacchi, C.; Capelo, A., Variational and quasi-variational inequalities, applications to free boundary problems, (1984), Wiley New York
[2] Chen, G.Y., Existence of solution for a vector variational inequality: an extension of the hartman – stampacchia theorem, J. optim. theory appl., 74, 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)
[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, (), 151-186
[6] Giannessi, F., On connections among separation, penalization and regularization for variational inequalities with point-to-set-operators, Rend. circ. mat. Palermo ser., II, Suppl. 48, 11-18, (1997)
[7] Giannessi, F., On minty variational principle, () · Zbl 0909.90253
[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), Academic Press New York · Zbl 0457.35001
[10] Kumari, A.; Mukherjee, R.N., On some generalized multi-valued variational inequalities, Indian J. pure appl. math., 31, 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, 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, 1, 33-41, (1997) · Zbl 0899.49005
[15] Nadler, S.B., 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, III, 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.