Zhang, Qing-Bang; Tang, Gusheng The property of the set of equilibria of the equilibrium problem with lower and upper bounds on Hadamard manifolds. (English) Zbl 1472.49014 Abstr. Appl. Anal. 2014, Article ID 329545, 5 p. (2014). Summary: The existence of equilibrium points, and the essential stability of the set of equilibrium points of the equilibrium problem with lower and upper bounds are studied on Hadamard manifolds. Cited in 1 Document MSC: 49J27 Existence theories for problems in abstract spaces 49J40 Variational inequalities 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics Keywords:Hadamard manifolds; equilibrium × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Blum, E.; Oettli, W., From optimization and variational inequalities to equilibrium problems, The Mathematics Student, 63, 1-4, 123-145 (1994) · Zbl 0888.49007 [2] Brezis, H.; Nirenberg, L.; Stampacchia, G., A remark on Ky Fan’s minimax principle, Bollettino della Unione Matematica Italiana, 6, 4, 293-300 (1972) · Zbl 0264.49013 [3] Bigi, G.; Castellani, M.; Pappalardo, M.; Passacantando, M., Existence and solution methods for equilibria, European Journal of Operational Research, 227, 1, 1-11 (2013) · Zbl 1292.90315 · doi:10.1016/j.ejor.2012.11.037 [4] Isac, G.; Sehgal, V. M.; Singh, S. P., An alternate version of a variational inequality, Indian Journal of Mathematics, 41, 1, 25-31 (1999) · Zbl 1034.49005 [5] Li, J., A lower and upper bounds version of a variational inequality, Applied Mathematics Letters, 13, 5, 47-51 (2000) · Zbl 1023.49003 [6] Chadli, O.; Chiang, Y.; Yao, J. C., Equilibrium problems with lower and upper bounds, Applied Mathematics Letters, 15, 3, 327-331 (2002) · Zbl 1175.90411 · doi:10.1016/S0893-9659(01)00139-2 [7] Ansari, Q. H.; Yao, J.-C., A fixed point theorem and its applications to a system of variational inequalities, Bulletin of the Australian Mathematical Society, 59, 3, 433-442 (1999) · Zbl 0944.47037 · doi:10.1017/S0004972700033116 [8] Fan, K., A generalization of Tychonoff’s fixed point theorem, Mathematische Annalen, 142, 3, 305-310 (1961) · Zbl 0093.36701 · doi:10.1007/BF01353421 [9] Zhang, C., A class of equilibrium problems with lower and upper bounds, Nonlinear Analysis: Theory, Methods & Applications, 63, 5-7, e2377-e2385 (2005) · Zbl 1224.90193 · doi:10.1016/j.na.2005.03.019 [10] Al-Homidan, S.; Ansari, Q. H., Systems of quasi-equilibrium problems with lower and upper bounds, Applied Mathematics Letters, 20, 3, 323-328 (2007) · Zbl 1114.49006 · doi:10.1016/j.aml.2006.04.016 [11] Fan, L., Weighted quasi-equilibrium problems with lower and upper bounds, Nonlinear Analysis: Theory, Methods & Applications, 70, 6, 2280-2287 (2009) · Zbl 1155.90453 · doi:10.1016/j.na.2008.03.007 [12] Mitrovi, Z. D.; Merkle, M., On a generalized vector equilibrium problem with bounds, Applied Mathematics Letters, 23, 7, 783-787 (2010) · Zbl 1218.49010 · doi:10.1016/j.aml.2010.03.009 [13] Colao, V.; López, G.; Marino, G.; Martín-Márquez, V., Equilibrium problems in Hadamard manifolds, Journal of Mathematical Analysis and Applications, 388, 1, 61-77 (2012) · Zbl 1273.49015 · doi:10.1016/j.jmaa.2011.11.001 [14] DoCarmo, M. P., Riemannian Geometry (1992), Boston, Mass, USA: Birkhäuser, Boston, Mass, USA · Zbl 0752.53001 [15] Chavel, I., Riemannian Geometry: A Modern Introduction, 108 (1993), Cambridge, Mass, USA: Cambridge University Press, Cambridge, Mass, USA · Zbl 0810.53001 [16] Zhou, L. W.; Huang, N. J., Generalized KKM theorems on Hadamard manifolds with applications [17] Yu, J., Game Theory and Nonlinear Analysis, Beijing, China: Science Press, Beijing, China [18] Fort,, M. K., Essential and non essential fixed points, American Journal of Mathematics, 72, 2, 315-322 (1950) · Zbl 0036.13001 · doi:10.2307/2372035 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.