Speaker
Description
Providing the existence of an intersection point for a family of sets is commonly useful in many problems. Various studies have been done in this regard within the framework of KKM theory. The concept of weak KKM has been applied in some papers within this objective. In these results, the existence of a solution is often linked to certain closedness and compactness conditions that are not satisfied in many real applications. On the other hand, various notions of pseudomonotonicity are applied to variational inequalities, optimization and other problems in nonlinear analysis. Here, first we introduce a new concept of topological pseudomonotonicity for a pair of set-valued maps. Then, applying this condition, we present an intersection theorem under relaxed closedness and coercivity conditions. Moreover, by introducing new concept of upper continuity for bifunctions, some applications of this result will be presented.
