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Generalized quasi-variational inequality and implicit complementarity problems

A new problem called the generalized quasi-variational inequality problem is introduced. This new formulation extends all kinds of variational inequality problem formulations that have been introduced and enlarges the class of problems that can be approached by the variational inequality problem formulation. Existence results without convexity assumptions are established and topological properties of the solution set are investigated. A new problem called the generalized implicit complementarity problem is also introduced which generalizes all the complementarity problem formulations that have been introduced. Applications of generalized quasi-variational inequality and implicit complementarity problems are given.