On System of Generalized Vector Quasi-equilibrium Problems with Set-valued Maps

Authors:
Jian-Wen Peng;Heung-Wing Joseph Lee;Xin-Min Yang
Affiliations:
Aff1 Aff2;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong;College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, P.R. China 400047
Venue:
Journal of Global Optimization
Year:
2006

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Abstract

In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions.