EXISTENCE THEOREMS OF GENERALIZED QUASI- AND BI-QUASI-VARIATIONAL INEQUALITIES FOR QUASI- AND BI-QUASI-MONOTONE OPERATORS WITH APPLICATIONS IN NON-COMPACT SETTINGS AND MINIMIZATION PROBLEMS

Abstract

In this paper we shall obtain some existence theorems of generalized quasi-variational and bi-quasi-variational inequalities for quasi-monotone and bi-quasi-monotone operators, respectively, in both compact and non-compact settings. Our results will extend and or generalize the corresponding results in [13] or [15].