Solvability based on E-property for the nonlinear symmetric cone complementarity problem

In this paper, we introduce some concepts of E-properties for nonlinear transformations defined on Euclidean Jordan algebras, such as E-property, quad E-property, uniform Jordan E-property, E0-property. And then we study the implications among these E-properties. In particular, the quad E-property is equivalent to the E-property. The KK-copositive property implies the E0-property. The uniform Jordan E-property is proved to have the E0 and R0-properties. Based on the E-properties, we get some sufficient conditions to guarantee the solution existence for the nonlinear symmetric cone complementarity problem.