In this paper, we establish several different versions of generalized Ekeland’s variational principle and maximal element theorem
for -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.