On Vector Equilibrium Problem with Generalized Pseudomonotonicity

Advances in Mathematical Finance and Applications

مقاله 5، دوره 4، شماره 2، مرداد 2019، صفحه 65-74   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/amfa.2019.583570.1170

نویسندگان

Ali Farajzadeh^{* 1}؛ Syyedeh Marzieh Halimi²

¹Department of Mathematics, Razi University, Kermanshah, 67149, Iran

²Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran,Iran

چکیده

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.

کلیدواژه‌ها

Economics equilibrium point؛ Vector equilibrium problem؛ Generalized pseudomonotonicity

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