×

zbMATH — the first resource for mathematics

Upper order-preservation of the solution correspondence to vector equilibrium problems. (English) Zbl 1434.49005
Summary: In this paper, several order-theoretic fixed point theorems are proved on partially ordered topological spaces. Applying these fixed point theorems, we explore the existence and upper order-preservation for parametric vector equilibrium problems. In contrast to the previous results on vector equilibrium problems, the upper order-preservation of solutions is a new subject, which would be useful for predicting the changing trend of solutions to vector equilibrium problems. In addition, neither topological continuity nor convexity of the considered vector-valued bifunction \(F\) is required in our results.
MSC:
49J40 Variational inequalities
47H10 Fixed-point theorems
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C48 Programming in abstract spaces
91B50 General equilibrium theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bianchi, M.; Hadjisavvas, N.; Schaible, S., Vector equilibrium problems with generalized monotone bifunctions, J Optim Theory App, 92, 3, 527-542, (1997) · Zbl 0878.49007
[2] Fu, J., Simultaneous vector variational inequalities and vector implicit complementarity problem, J Optim Theory App, 93, 1, 141-151, (1997) · Zbl 0901.90169
[3] Chadli, O.; Chiang, Y.; Huang, S., Topological pseudomonotonicity and vector equilibrium problems, J Math Anal Appl, 270, 2, 435-450, (2002) · Zbl 1007.90077
[4] Li, J.; Huang, Nj; Kim, J., On implicit vector equilibrium problems, J Math Anal Appl, 283, 2, 501-512, (2003) · Zbl 1137.90715
[5] Farajzadeh, Ap; Amini-Harandi, A., On the generalized vector equilibrium problems, J Math Anal Appl, 344, 2, 999-1004, (2008) · Zbl 1147.49005
[6] Cap, A., Existence results for globally efficient solutions of vector equilibrium problems via a generalized KKM principle, Acta Math Sci, 37, 2, 463-476, (2017) · Zbl 1389.90320
[7] Ansari, Qh; Yao, Jc., An existence result for the generalized vector equilibrium problem, Appl Math Lett, 12, 8, 53-56, (1999) · Zbl 1014.49008
[8] Ansari, Qh; Konnov, Iv; Yao, Jc., On generalized vector equilibrium problems, Acta Math Appl, 47, 1, 543-554, (2006)
[9] Ansari, Qh; Flores-Bazan, F., Generalized vector quasi-equilibrium problems with applications, J Math Anal Appl, 277, 1, 246-256, (2003) · Zbl 1022.90023
[10] Ansari, Qh; Schaible, S.; Yao, Jc., The system of generalized vector equilibrium problems with applications, J Global Optim, 22, 1-4, 3-16, (2002) · Zbl 1041.90069
[11] Lashkaripour, R.; Karamian, A., On a new generalized symmetric vector equilibrium problem, J Inequal Appl, 2017, 1, 237, (2017) · Zbl 1376.49010
[12] Bianchi, M.; Kassay, G.; Pini, R., Ekeland’s principle for vector equilibrium problems, Nonlinear Anal, 66, 7, 1454-1464, (2007) · Zbl 1110.49007
[13] Gong, X., Ekeland’s principle for set-valued vector equilibrium problems, Acta Math Sci, 34, 4, 1179-1192, (2014) · Zbl 1324.49014
[14] Gutiérrez, C.; Kassay, G.; Novo, V., Ekeland variational principles in vector equilibrium problems, SIAM J Optim, 27, 4, 2405-2425, (2017) · Zbl 1381.58007
[15] Zhang, C.; Wang, Y., Applications of order-theoretic fixed point theorems to discontinuous quasi-equilibrium problems, Fixed Point Theory Appl, 2015, 54, (2015) · Zbl 1338.47070
[16] Anh, Lq; Khanh, Pq., Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems, J Math Anal Appl, 294, 699-711, (2004) · Zbl 1048.49004
[17] Anh, Lq; Khanh, Pq., Semicontinuity of solution sets to parametric quasivariational inclusions with applications to traffic networks II. Lower semicontinuities applications, Set-Valued Anal, 16, 943-960, (2008) · Zbl 1156.90443
[18] Anh, Lq; Khanh, Pq., Sensitivity analysis for weak and strong vector quasiequlibrium problems, Vietnam J Math, 37, 237-253, (2009)
[19] Anh, Lq; Khanh, Pq., Continuity of solution maps of parametric quasiequilibrium problems, J Global Optim, 46, 247-259, (2010) · Zbl 1187.90284
[20] Li, Sj; Li, Xb; Wang, Ln, The Hölder continuity of solutions to generalized vector equilibrium problems, Eur J Oper Res, 199, 2, 334-338, (2009) · Zbl 1176.90643
[21] Zhang, Wy; Fang, Zm; Zhang, Y., A note on the lower semicontinuity of efficient solutions for parametric vector equilibrium problems, Appl Math Lett, 26, 4, 469-472, (2013) · Zbl 1264.90156
[22] Han, Y.; Gong, Xh., Lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems, Appl Math Lett, 28, 2, 38-41, (2014) · Zbl 1311.90153
[23] Anh, Lq; Khanh, Pq; Tam, Tn., On Hölder continuity of approximate solutions to parametric equilibrium problems, Nonlinear Anal, 75, 2293-2303, (2012) · Zbl 1237.49032
[24] Anh, Lq; Khanh, Pq; Tam, Tn., Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems, TOP, 24, 242-258, (2016) · Zbl 1343.49040
[25] Anh, Lq; Duoc, Pt; Tam, Tn., Continuity of approximate solution maps to vector equilibrium problems, J Ind Manag Optim, 13, 2, 1-13, (2017)
[26] Nishimura, H.; Ok, Ea., Solvability of variational inequalities on Hilbert lattices, Math Oper Res, 37, 4, 608-625, (2012) · Zbl 1297.90155
[27] Sun, Sq., Order preservation of solution correspondence to single-parameter generalized variational inequalities on Hilbert lattices, J Fix Point Theory A, 19, 3, 1-14, (2017)
[28] Wang, Y.; Zhang, C., Order-preservation of solution correspondence for parametric generalized variational inequalities on Banach lattices, Fixed Point Theory Appl, 2015, 108, (2015) · Zbl 06583521
[29] Meyer-Nieberg, P., Banach lattices, (1991), Berlin: Springer, Berlin · Zbl 0743.46015
[30] Schaefer, Hh., Topological vector spaces, (1970), New York: Springer, New York
[31] Li, J.; Ok, Ea., Optimal solutions to variational inequalities on Banach lattices, J Math Anal Appl, 388, 1157-1165, (2012) · Zbl 1231.49011
[32] Huang, Nj; Li, J.; Thompson, Hb., Implicit vector equilibrium problems with applications, Math Comput Model, 37, 1343-1356, (2003) · Zbl 1080.90086
[33] Fujimoto, T., An extension of Tarski’s fixed point theorem and its application to isotone complementarity problems, Math Program, 28, 116-118, (1984) · Zbl 0526.90084
[34] Li, D.; Nagurney, A., A general multitiered supply chain network model of quality competition with suppliers, Int J Prod Econ, 170, 336-356, (2015)
[35] Vector equilibrium problems and vector variational inequalitiesVector variational inequalities and vector equilibria. Nonconvex optimization and its applicationsBoston, MASpringer2000
[36] Chadli, O.; Riahi, H., On generalized vector equilibrium problems, J Global Optim, 16, 1, 69-75, (2000) · Zbl 0966.60003
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.