Well-posedness Of A Generalized Mixed Variational Inequality In Banach Spaces

In this thesis, we first introduce the concept of Levitin-Polyak well-posedness of a generalized mixed variational inequality and establish its metric characterizations in Banach spaces. Under some suitable conditions, we prove that the Levitin-Polyak well-posedness of a generalized mixed variational inequality is equivalent to the Levitin-Polyak well-posedness of a corresponding inclusion problem and a corresponding fixed point problem. Secondly, we present the Hadamard well-posedness of a general mixed variational inequality, besides, we investigate the equivalent relationship between the Hadamard well-posedness and Levitin-Polyak well-posedness of a general mixed varia-tional inequality. Finally, we derive some metric characterizations for the Levitin-Polyak well-posedness by perturbations of a generalized vector mixed variational inequality, we also prove the equivalent relationship between the Levitin-Polyak well-posedness by perturbations of a generalized vector mixed variational inequality and the gap function of a minimizing problem.