Generalized R-KKM theorems in topological space and their applications ✩

In this paper, we introduce generalized R-KKM mapping and discuss some new generalized RKKM theorem under the nonconvexity setting of topological space. As applications, some new minimax inequalities, saddle point theorem are proved in topological space. Our theorems unified and extend many known results in recent literature.  2003 Elsevier Inc. All rights reserved.