×

Vector mixed quasi complementarity problems in Banach spaces. (English) Zbl 1255.90115

Summary: We introduce a new class of set-valued vector implicit quasi complementarity problems with corresponding set-valued implicit quasi variational inequality problems. By means of the Fan-KKM theorem, we investigate the nonemptiness and compactness of solution sets of these problems. Our work generalizes and improves some results appeared recently in the literature.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C31 Sensitivity, stability, parametric optimization
49J40 Variational inequalities
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Lemke, C.E., Bimatrix equilibrium points and mathematical programming, Management sci., 11, 681-689, (1965) · Zbl 0139.13103
[2] Cottle, R.W.; Dantzig, G.B., Complementarity pivot theory of mathematical programming, Linear algebra appl., 1, 163-185, (1968) · Zbl 0208.45503
[3] Chen, G.Y.; Yang, X.Q., The vector complementarity problems and its equivalences with the weak minimal element in ordered spaces, J. math. anal. appl., 153, 136-158, (1990) · Zbl 0712.90083
[4] Farajzadeh, A.P.; Zafarani, J., Vector \(F\)-implicit complementarity problems in topological vector spaces, Appl. math. lett., 20, 1075-1081, (2007) · Zbl 1189.90171
[5] Farajzadeh, A.P.; Noor, M.A.; Zainab, S., Mixed quasi complementarity problems in topological vector spaces, J. global optim., 45, 229-235, (2009) · Zbl 1193.90204
[6] Huang, N.J.; Li, J., \(F\)-implicit complementarity problems in Banach spaces, Z. anal. anwend., 23, 293-302, (2004) · Zbl 1135.90412
[7] Karamardian, S., Generalized complementarity problem, J. optim. theory appl., 8, 161-168, (1971) · Zbl 0218.90052
[8] Khan, S.A., Generalized vector complementarity-type problems in topological vector spaces, Comput. math. appl., 59, 3595-3602, (2010) · Zbl 1197.49005
[9] Khan, S.A., Generalized vector implicit quasi complementarity problems, J. global optim., 49, 695-705, (2011) · Zbl 1242.90261
[10] Lee, B.S.; Farajzadeh, A.P., Generalized vector implicit complementarity problems with corresponding variational inequality problems, Appl. math. lett., 21, 1095-1100, (2008) · Zbl 1211.90249
[11] Lee, B.S.; Khan, M.F.; Salahuddin, Vector \(F\)-implicit complementarity problems with corresponding variational inequality problems, Appl. math. lett., 20, 433-438, (2007) · Zbl 1180.90338
[12] Li, J.; Huang, N.J., Vector \(F\)-implicit complementarity problems in Banach spaces, Appl. math. lett., 19, 464-471, (2006) · Zbl 1111.90109
[13] Yang, X.Q., Vector complementarity and minimal element problems, J. optim. theory appl., 77, 483-495, (1993) · Zbl 0796.49014
[14] Aubin, J.-P.; Frankowska, H., Set-valued analysis, (1990), Birkhauser Boston
[15] Fan, K., A generalization of tychonoff’s fixed point theorem, Math. ann., 142, 305-310, (1961) · Zbl 0093.36701
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.