Exceptional families of elements for set-valued mappings: An application to nonlinear complementarity problems

In this work, based upon the topological degree for set-valued mappings, instead of the Leray–Schauder type alternative and the technique of continuous selection, the notion of an exceptional family of elements for set-valued mappings in Isac’s sense is applied to nonlinear complementarity problems (for short, S-CP(F,K,H)) and an existence result for solutions for S-CP(F,K,H) is obtained.