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On maximal element theorems, variants of Ekeland’s variational principle and their applications. (English) Zbl 1133.58006
Summary: We establish several different versions of the generalized Ekeland’s variational principle and maximal element theorem for τ-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.
58E30Variational principles on infinite-dimensional spaces
49J35Minimax problems (existence)
54H25Fixed-point and coincidence theorems in topological spaces