On four discrete-type families of NCP-functions

In this paper, we look into the detailed properties of four discrete- type families of NCP-functions, which are newly discovered in recent literature. With the discrete-oriented feature, we are motivated to know what differences there are compared to the traditional NCP-functions. The properties obtained in this paper not only explain the difference but also provide background bricks for designing solution methods based on such discrete-type families of NCP- functions.