Gap functions and existence of solutions for generalized vector quasivariational inequalities. (English) Zbl 1142.49303

Long, Xian Jun; Huang, Nan Jing

Involve 1, No. 2, 183-195 (2008).

Summary: The gap functions for generalized vector quasivariational inequalities in Hausdorff topological vector spaces are introduced, then using Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem, some existence theorems for a class of generalized vector quasivariational inequalities under suitable assumptions are established. The obtained results extend and unify corresponding results in the literature.

MSC:

49J40	Variational inequalities
47H04	Set-valued operators
47J20	Variational and other types of inequalities involving nonlinear operators (general)

Keywords:

generalized vector quasivariational inequality; gap function; existence of solutions; FKKM theorem; set-valued mapping