The Idzik type quasivariational inequalities and noncompact optimization problems
Sehie Park, Jong Moon Park · Colloquium Mathematicum · 1996
A quasi-variational inequality theorem equivalent to the Idzik fixed point theorem is obtained. Partial generalizations to condensing maps are also obtained. Those are applied to give simple and unified proofs of a number of wellknown variational inequalities of the Hartman-Stampacchia-Browder type, and to solve a noncompact infinite optimization problem, which leads us to a generalized Nash equilibrium theorem. Supported in part by Ministry of Education, 1995, Project Number BSRI-95-1413.