On Vector Equilibrium Problem with Generalized Pseudomonotonicity
محورهای موضوعی : Econometrics and Financial Applications of other Theories (Stochastic Processes, (Stochastic) Partial Differential Equations, Dynamical Systems)Ali Farajzadeh 1 , Syyedeh Marzieh Halimi 2
1 - Department of Mathematics, Razi University, Kermanshah, 67149, Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran,Iran
کلید واژه: Economics equilibrium point, Vector equilibrium problem, Generalized pseudomonotonicity,
چکیده مقاله :
In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$\acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonotonicity for vector valued bifunctions is introduced. By using it some existence results for the vector equilibrium problem, in the setting of topological vector spaces, are presented. Some examples in order to illustrate the main results and compare them with the corresponding published results are furnished. Further, the compactness of the solution set of vector equilibrium problem is investigated.
[1] Ansari, Q. H., Farajzadeh A.P., Schaible, S., Existence of solutions of strong vector equilibrium problems, Taiw. J. Math., 2012, 16(1), P.165-178. Doi:10.11650/twjm/1500406534
[2] Aubin, J.P., Ekeland, I., Applied Nonlinear Analysis, John Wiley and Sons, 1984.
[3] Bai, M. R., Zhou, S. Z. and Ni, G. Y., Variational-like inequalities with relaxed η − α pseudomonotone mappings in Banach spaces, Appl. Math. Lett., 2006, 19, P.547-554. Doi:10.1016/j.aml.2005.07.010
[4] Blum, E., Oettli, W., From optimization and variational inequalities to equilibrium problems, Math. Stud,1994, 63, P.123-145.
[5] Cournot, A., Theorie mathematique de la richesse sociale and of recherches surles principles mathematiques de la theorie des richesses, Paris, 1838.
[6] Dalvand,KH., Tabatabaie, M.,Studying the Role of Marketing Intensity on the Relation of Financial Leverage and Firm Function, Adv. Math. Fin. Appl., 2018, 3(3), P.27-39. Doi: 10.22034/ AMFA.2018.544947
[7] Creedy, J., The Foundations of Economic Thought, Blackwells, 1990.
[8] Fan, K., Some properties of convex sets related to fixed point theorems, Math. Ann., 1984, 266, P.519-537. Doi:10.1007/BF01458545
[9] Farajzadeh, A.P., Noor, M.A., Generalized mixed quasicomplementary problems in topological vector spaces, The Anziam J., 2008, 49(4), P.525-531
[10] Farajzadeh,A., Plubtieng,S., Hosseinpour, A., On the existence of solutions of generalized equilibrium problems with monotone mappings, J. Nonlin. Sci. Appl., 2016, 9(10), P.5712-5719. Doi:10.2243 6/jnsa.009.10.16
[11] Farajzadeh, A.P., Zafarani, J., Equilibrium problems and variational inequalities in topological vector, Optimization, 2010, 59(4), P.485-499, Doi: 10.1080/02331930801951090
[12] Iusem, A.N., Sosa, W., New existence results for equilibrium problems, Nonlin. Anal., 2003, 52, P.621-635 .Doi:10.1016/S0362-546X(02)00154-2
[13] Khorshidvand, F., Sarlak, A., Examining the Relationship between Corporate Governance and the Corporate Performance Valuation, Advances in mathematical finance and applications, 2017, 2(3), P.29-39. Doi:10. 22034/AMFA.2017.533097
[14] Luc, D.T., Theory of Vector Optimization, Springer-Verlag, Germany, 1989.
[15] Mahato, N.K., Nahak, C., Weakly relaxed -pseudomonotonicity and equilibrium problem in Banach spaces, J. Appl. Math. Comput, 2012, 40, P.499-509. Doi: 10.1007/s12190-012-0584-6
[16] Mahato, N.K., Nahak, C.,Vector eqilibrum problems with new types of generalized monotnicity , Yugoslav J. Operation Research, 2013, 23, P.213-220,Doi: 10.2298/YJOR130107024M
[17] Najfi Moghaddam, A., Aslani, D., Impacts of Cash Dividend Components on Earning Persistence and Return on Stock, Advances in mathematical finance and applications, 2018, 3(1), P.53-67. Doi: 10.22034/AMFA .2018.539134
[18] Peressini, A.L., Ordered Topological Vector Spaces, Harper and Row, New York, 1967.
[19] Turnovsky, S.J., Methods of Macroeconomic Dynamics. MIT Press, 2000.
[20] Varian ,H.R., Microeconomic Analysis (Third ed.), New York, 1992.
