Variational relation problem without the KKM property with applications

In this paper, we will study variational relation problems without the KKM property, whose proof techniques differ between Luc (2008) [1] and Pu and Yang (2012) [9]. As applications, some existence theorems of solution for the generalized KKM theorem, variational inclusion problem, generalized (vector) Ky Fan Minimax Inequality, generalized Ky Fan section theorem, nn-person noncooperative generalized game and nn-person noncooperative multi-objective generalized game are obtained.