ABSTRACT
As applications of Ky Fan minimax principle and Kneser’s minimax theorem, the existence theorems of solutions of variational inequalities for monotone and quasi-monotone set-valued mapping in either topological vector spaces or reflexive Banach spaces have been established. These results are then used to study the existence of solutions for generalized complementarity problems; and some fixed point theorems for set-valued quasi-contractive mappings which are generalizations of pseudo-contractive nonexpansive mappings (which, in turn are generalizations of nonexpansive mappings) are obtained. Finally existence theorems on minimizers of minimization problem for the sum of convex lower semicontinuous functions are established. These results include corresponding results of literatures as special cases.
