Abstract Generalized Variational Inequality and Applications in the G-convex Space
HE Rong-hua · Journal of Sichuan Normal University · 2005
In this paper, a generalized RKKM type nonempty intersection theorem is established under the noncompact setting of G-convex space.By using a known fixed point theorm and the nonempty intersection theorem,an existence theorm of solutions for abstract generalized variational inequalities is proved in noncompact G-convex space. As applications, we prove an existence theorm of saddle point in G-convex space. These theorems are all new and improve some known results in recent literature.