On System of Generalized Vector Quasi-equilibrium Problems with Set-valued Maps |
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| Authors: | Jian-Wen Peng Heung-Wing Joseph Lee Xin-Min Yang |
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| Institution: | (1) College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, P.R. China;(2) Department of Management Science, School of Management, Fudan University, Shanghai, 200433, P. R.China;(3) Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
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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. |
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| Keywords: | C i-x -0-partially diagonally quasiconvex generalized Debreu type equilibrium problem maximal element theorem Φ -condensing map system of generalized vector quasi-equilibrium problems system of vector quasi-equilibrium problems |
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