The System of Vector Quasi-Equilibrium Problems with Applications

  • Authors:

  • Q. H. Ansari;W. K. Chan;X. Q. Yang

  • Affiliations:

  • Department of Mathematical Sciences, King Fahd University of Petroleum &/ Minerals, P.O. Box 1169, Dhahran 31261, Saudi Arabia/ and Department of Mathematics, Aligarh Muslim University, Aligarh ...;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong (e-mail: machanwk@polyu.edu.hk);Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong (e-mail: mayangxq@polyu.edu.hk)

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2004

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Abstract

In this paper, we consider the system of vector quasi-equilibrium problems with or without involving Φ-condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibrium problem for vector-valued functions. As an application, we derive some existence results for a solution to the Debreu type equilibrium problem for vector-valued functions.