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New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces
Authors:Chih-Sheng Chuang  Lai-Jiu Lin
Institution:1. Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan
2. Department of Mathematics, National Chang kung University, Tainan, 701, Taiwan
Abstract:Motivated by the Suzuki’s type fixed point theorems, we give several new existence theorems for scalar quasi-equilibrium problems, and vector quasi-equilibrium problem on complete metric spaces. We give important examples for our results. Note that the solution of quasi-equilibrium problem (resp. vector quasi-equilibrium problem) is unique under suitable conditions, and we can find the unique solution by the Picard iteration. Besides, we also give a new coincidence theorem on complete metric spaces. Finally, we give a new minimax theorem on complete metric spaces. Note that the solution of minimax theorem is unique under suitable conditions, and we can find the unique solution by the Picard iteration.
Keywords:
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