By considering the notion of regular exceptional family of elements (REFE), we define the class of REFE-acceptable mappings. By definition, a complementarity problem on a Hilbert space defined by a REFE-acceptable mapping and a closed convex cone has either a solution or a REFE. We present several classes of REFE-acceptable mappings. For this, neither the topological degree nor the Leray-Schauder alternative is necessary. By using the concept of REFE-acceptable mappings, we present necessary and sufficient conditions for the nonexistence of regular exceptional family of elements. These conditions are used for generating several existence theorems and existence and uniqueness theorems for complementarity problems.
- regular exceptional family of elements
- REFE-acceptable mappings
- nonlinear complementarity problems