Abstract

The authors have introduced a general quasi-optimization problem through multivalued mappings which play an important role in the theory of vector optimization. These are related to six different quasi-equilibrium problems namely upper/lower ideal quasi-equilibrium problem, upper/lower Pareto quasi-equilibrium problem, upper/lower weak quasi-equilibrium problem. They finally state upper/lower quasivariational inclusion problem of type I and establish some new results on existence theorems under weak conditions thereby improving the results of the second author [J. Optimization Theory Appl. 123, No. 3, 619–638 (2004; Zbl 1059.49020)].