The notion of exceptional family of elements for general order complementarity problems in Banach spaces will be introduced. It will be shown that for general order complementarity problems defined by completely continuous fields the problem has either a solution or an exceptional family of elements. Finite dimensional examples and an application to integral operators will be given. (C) 2010 Elsevier Inc. All rights reserved.
- Integral operator
- Vector lattice
- Exceptional family of elements
- General order complementarity problem
- Ordered Banach space
- Leray-Schauder alternative