Solvability of implicit complementarity problems

In this paper, a new notion of exceptional family of elements (EFE) for a pair of functions involved in the implicit complementarity problem (ICP) is introduced. Based upon this notion and the Leray-Schauder Alternative, a general alternative is obtained which gives more general existence theorems for the implicit complementarity problem. Finally, via the techniques of continuous selections, these existence theorems are extended to the multi-valued implicit complementarity problems (MIPS).