Lin, Lai-Jiu; Park, Sehie On some generalized quasi-equilibrium problems. (English) Zbl 0924.49008 J. Math. Anal. Appl. 224, No. 2, 167-181 (1998). The authors have used the fixed point technique to obtain some existence results for equilibrium, quasi-equilibrium and generalized quasi-equilibrium problems in \(G\)-convex spaces settings. The results obtained in this paper extend and improve the previously known results in this fields. Reviewer: Muhammad Aslam Noor (Riyadh) Cited in 53 Documents MSC: 49J40 Variational inequalities 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:equilibrium problems; variational inequalities; fixed points; existence results; quasi-equilibrium problems PDFBibTeX XMLCite \textit{L.-J. Lin} and \textit{S. Park}, J. Math. Anal. Appl. 224, No. 2, 167--181 (1998; Zbl 0924.49008) Full Text: DOI Link References: [1] Berge, C., Espaces Topologiques (1959), Dunod: Dunod Paris · Zbl 0088.14703 [2] Blum, E.; Oettli, W., From optimization and variational inequalities to equilibrium problems, Math. Student, 63, 123-145 (1994) · Zbl 0888.49007 [3] Chang, S. S.; Lee, B. S.; Wu, X.; Cho, Y. J.; Lee, G. M., On the generalized quasi-variational inequality problems, J. Math. Anal. Appl., 203, 686-711 (1990) [4] Chen, M. P.; Park, S., A unified approach to generalized quasi-variational inequalities, Comm. Appl. Nonlinear Anal., 4, 103-118 (1997) · Zbl 0878.49005 [5] Hadžić, O., Fixed point theory in topological vector spaces (1984), University of Novi Sad: University of Novi Sad Novi Sad · Zbl 0576.47030 [6] Horvath, C. D., Extensions and selection theorems in topological spaces with a generalized convexity structure, Ann. Fac. Sci. Toulouse, 2, 253-269 (1993) · Zbl 0799.54013 [7] Klee, V., Leray-Schauder theory without local convexity, Math. Ann., 141, 286-297 (1960) · Zbl 0096.08001 [8] Kum, S., A generalization of generalized quasi-variational inequalities, J. Math. Anal. Appl., 182, 158-164 (1994) · Zbl 0804.49012 [9] Noor, M. A.; Oettli, W., On general nonlinear complementarity problems and quasi-equilibria, Le Matematiche, 49, 313-331 (1994) · Zbl 0839.90124 [10] Park, S., Some coincidence theorems on acyclic multifunction and application to KKM theory, (Tan, K. K., Fixed Point Theory and Applications (1992), World Scientific: World Scientific River Edge), 248-277 · Zbl 1426.47005 [11] S. Park, Fixed points and quasi-equilibrium problems, Math. Comp. Modelling; S. Park, Fixed points and quasi-equilibrium problems, Math. Comp. Modelling · Zbl 0983.47038 [12] S. Park, Remarks on a social equilibrium existence theorem of G. Debreu, Appl. Math. Lett.; S. Park, Remarks on a social equilibrium existence theorem of G. Debreu, Appl. Math. Lett. · Zbl 1116.91329 [13] Park, S.; Chen, M.-P., Generalized quasi-variational inequalities, Far East J. Math. Sci., 3, 185-190 (1995) [14] Park, S.; Kim, H., Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl., 197, 173-187 (1996) · Zbl 0851.54039 [15] Park, S.; Kim, H., Foundations of the KKM theory on generalized convex spaces, J. Math. Anal. Appl., 209, 551-571 (1997) · Zbl 0873.54048 [16] Tan, K.-K.; Zhang, X.-L., Fixed point theorems on \(G\), Proc. Nonlinear Funct. Anal. Appl., 1, 1-19 (1996) [17] Weber, H., Compact convex sets in non-locally-convex spaces, Note die Math., 12, 271-289 (1992) · Zbl 0846.46004 [18] Yao, J. C., On generalized variational inequality, J. Math. Anal. Appl., 174, 550-555 (1993) · Zbl 0792.49009 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.