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On Vector Equilibrium Problem with Generalized Pseudomonotonicity

فصلنامه پیشرفتهایی در ریاضیات مالی و کاربردها، دوره: 4، شماره: 2
Year: 1398
COI: JR_AMFA-4-2_005
Language: EnglishView: 40
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Ali Farajzadeh - Department of Mathematics, Razi University, Kermanshah, ۶۷۱۴۹, Iran
Syyedeh Marzieh Halimi - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran,Iran


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.


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Farajzadeh, Ali and Halimi, Syyedeh Marzieh,1398,On Vector Equilibrium Problem with Generalized Pseudomonotonicity,

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  • Ansari, Q. H., Farajzadeh A.P., Schaible, S., Existence of solutions ...
  • Bai, M. R., Zhou, S. Z. and Ni, G. Y., ...
  • Cournot, A., Theorie mathematique de la richesse sociale and of ...
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  • Fan, K., Some properties of convex sets related to fixed ...
  • Mahato, N.K., Nahak, C., Weakly relaxed -pseudomonotonicity and equilibrium problem ...
  • Turnovsky, S.J., Methods of Macroeconomic Dynamics. MIT Press, ۲۰۰۰ ...
  • Varian ,H.R., Microeconomic Analysis (Third ed.), New York, ۱۹۹۲ ...

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