Applications of order-theoretic fixed point theorems to discontinuous quasi-equilibrium problems

In this paper, we apply order-theoretic fixed point theorems and isotone selection theorems to study quasi-equilibrium problems. Some existence theorems of solutions to quasi-equilibrium problems are obtained on Hilbert lattices, chain-complete lattices and chain-complete posets, respectively. In contrast to many papers on equilibrium problems, our approach is order-theoretic and all results obtained in this paper do not involve any topological continuity with respect to the considered mappings.