A study of multivalued variational inequalities via horizon maps and graphical convergence

Abstract

Multivalued variational inequalities is an active research area that encompasses many important models in mathematics, for example in optimization, fixed point, saddle point and complementary problems. The primary objective of this work is to apply horizon maps and graphical convergence to obtain existence and stability results for these problems. We give an exhaustive list of new results for these problems in terms of horizon maps and graphical convergence. Finally, we apply these results to the pseudomonotone and maximal monotone cases, establishing new formulations of known results in terms of these tools.