Gap functions and error bounds for generalized extended mixed vector equilibrium problem

Equilibrium problems are very important mathematical models and are closely related with fixed point problems, variational inequalities and nash equilibrium problems. Gap functions and error bounds which play a vital role in algorithms design, are two much-addressed topics of vector equilibrium problems. This paper deals with generalized extended mixed vector equilibrium problems. Without any scalarization approach, the gap functions and their regularized versions for generalized extended mixed vector equilibrium problems are first obtained. Then, in the absence of the projection operator method, some error bounds for generalized extended mixed vector equilibrium problems are established in terms of these regularized gap functions. The results obtained in this paper are in more simpler form from the computational point of view.