Existence Theorems of Solutions for Generalized Quasi-variational Inequalities, a Minimax Theorem, and a Section Theorem in the Spaces without Linear Structure*

In this paper, by using particular techniques, two existence theorems of solutions for generalized quasi-variational inequalities, a minimax theorem, and a section theorem in the spaces without linear structure are established; and finally, a new coincidence theorem in locally convex spaces is obtained.