New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces |
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Authors: | Chih-Sheng Chuang Lai-Jiu Lin |
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Institution: | 1. Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan 2. Department of Mathematics, National Chang kung University, Tainan, 701, Taiwan
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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. |
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