Alternative Theorems for Nonlinear Projection Equations and Applications to Generalized Complementarity Problems

Abstract

. This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a unified formulation of several special cases such as finite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems, and then two sufficient existence conditions, are established for this class of nonlinear projection equations. We use one of the alternative theorems to establish several new existence results for generalized complementarity problems with new classes of functions such as quasi-P , and P (ø; ff; fi)-maps. The class of quasi-P -maps is broad enough to encompass the union of quasi-monotone maps and nonlinear P -maps. The existence results established here significantly relax several previous solution conditions in the literature. Key words. Nonlinear projection equations, variational inequalities, generalized complementarity problems, exceptional families. 1 The research of this author i..