Gap Functions of a Kind of Hartman-Stampacchia Mutivalued Vector Variational-like Inequalities

Gap function is a powerful tool for translating variational inequalities into optimization problems, and is widely used to research the nonempty and the stability of variational inequality results. The strong Hartman and Stampacchia mutivalued vector variational-like inequality (SHSVL for short) and the weak Hartman and Stampacchia mutivalued vector variational-like inequality (WHSVL for short) are investigated. Furthermore, the gap functions of SHSVL and WHSVL that have mutivalued mapping are discussed by means of quantification.