On maximal element theorems, variants of Ekeland’s variational principle and their applications

In this paper, we establish several different versions of generalized Ekeland’s variational principle and maximal element theorem for ττ-functions in ≲≲ complete metric spaces. The equivalence relations between maximal element theorems, generalized Ekeland’s variational principle, generalized Caristi’s (common) fixed point theorems and nonconvex maximal element theorems for maps are also proved. Moreover, we obtain some applications to a nonconvex minimax theorem, nonconvex vectorial equilibrium theorems and convergence theorems in complete metric spaces.