Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems. (English) Zbl 1355.47023
Summary: We consider five different types of systems of generalized vector quasi-equilibrium problems and establish relationships among them by using different kinds of generalized pseudomonotonicities. We prove the existence of their solutions under lower semicontinuity for a family of multivalued maps involved in the formulation of these problems. The existence of solutions of these problems is also investigated without any coercivity condition but for \(\varPhi \)-condensing maps. We also establish some existence results for solutions of these problems under pseudomonotonicities in the setting of Hausdorff topological vector spaces as well as real Banach spaces.
MSC:
| 47J22 | Variational and other types of inclusions |
| 47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |
| 49J40 | Variational inequalities |
Keywords:
systems of generalized implicit vector quasi-equilibrium problems; generalized pseudomonotonicity; existence results; \(u\)-hemicontinuity; \(\mathcal H\)-hemicontinuity; lower semicontinuity; \(\varPhi \)-condensing mapsReferences:
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