Existence of Solutions for Abstract Economic Equilibrium Problems and Algorithm

Authors:
Cong-Jun Zhang;Jinlu Li;Min Sun
Affiliations:
Department of Applied Mathematics, Nanjing University of Finance and Economics Nanjing, Jiangsu 210003, P.R. China;Department of Mathematics, Shawnee State University 940 Second Street, Portsmouth, OH 45662, U.S.A.;Department of Applied Mathematics, Nanjing University of Finance and Economics Nanjing, Jiangsu 210003, P.R. China
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 4
Cited 0

Existence of solutions for a vector variational inequality: an extension of the Hartmann-Stampacchia theorem

Journal of Optimization Theory and Applications
On vector variational inequalities

Journal of Optimization Theory and Applications
Characterization of solutions for vector equilibrium problems

Journal of Optimization Theory and Applications
New existence results for equilibrium problems

Nonlinear Analysis: Theory, Methods & Applications

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Abstract

In this paper, we study a new kind of vector equilibrium problem and we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and Fan KKM theorem. Then we generalize this kind of vector equilibrium problem to a more general case. Equilibrium problems with lower and upper bounds was an open problem proposed by Isac, Sehgal and Singh in 1999. J. Li, O. Chadli, Y. Chiang and J.C. Yao, Zhang Cong-jun derived some results of the equilibrium problems with lower and upper bounds under certain conditions. In this paper we derive more results of this open problem under certain conditions, constructs an iteration algorithm, and discuses the convergence of the algorithm.