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Ekeland type variational principle with applications to quasi-variational inclusion problems |
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| Authors: | Lai-Jiu Lin Chih-Sheng Chuang |
| Institution: | a Department of Mathematics, National Changhua University of Education, Changhua 50058, Taiwan, ROC b Department of Mathematics, National Changhua University of Education, Changhua 50058, Taiwan, ROC c Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals, P.O. Box 119, Dhahran, Saudi Arabia |
| Abstract: | In this paper, we study the Ekeland type variational principle, a Caristi-Kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces. By using these results, we establish some existence results for solutions of quasi-variational inclusion problems, quasi-optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces. |
| Keywords: | Ekeland type variational principle Caristi-Kirk type fixed point theorem Quasi-variational inclusion problems Quasi-equilibrium problems Quasi-optimization problems Uniformly spaces Lower semicontinuity Sequentially lower monotone maps |
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