Some P-Properties for Nonlinear Transformations on Euclidean Jordan Algebras

In this article, we introduce the concepts of P and P₀ properties for a nonlinear transformation defined on a Euclidean Jordan algebra and study existence of solution in the associated complementarity problems. In particular, we show, in this general setting, that if a transformation has the P₀ and R₀ properties, then all associated complementarity problems have solutions. We also describe a necessary condition for a transformation to have the (global) uniqueness of solution property.