A fixed point theorem and its applications to a system of variational inequalities
Qamrul Hasan Ansari, Jen‐Chih Yao · Bulletin of the Australian Mathematical Society · 1999
In this paper, we first prove a fixed point theorem for a family of multivalued maps defined on product spaces. We then apply our result to prove an equilibrium existence theorem for an abstract economy. We also consider a system of variational inequalities and prove the existence of its solutions by using our fixed point theorem.