Generalized R-KKM type theorems in topological spaces with applications

In this work, some new generalized R-KKM type theorems for generalized R-KKM mappings with compactly open values are established in topological spaces without any convexity assumptions. As applications, a Ky Fan type matching theorem, fixed point theorem and coincidence theorem are obtained in topological spaces. These results generalize some known results from the recent literature.