Continuous selection theorem, coincidence theorem, and generalized equilibrium in L-convex spaces

In this paper, a new continuous selection theorem is first proved in L-convex spaces without linear structure. By using the continuous selection theorem, some new coincidence theorems, fixed-point theorems, and minimax inequality are proved in L-convex spaces. As applications, some new existence theorems of solutions for generalized equilibrium problems are obtained in L-convex spaces. These theorems improve and generalize some known results in recent literature.