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Equivalence between Ekeland’s variational principle and Caristi’s fixed point theorem. (Chinese. English summary) Zbl 0621.54030

This paper gives a direct proof of the equivalence between Ekeland’s variational principle and Caristi’s fixed point theorem, and proposes a formally stronger Caristi’s fixed point theorem. By this theorem, we can improve Clarke’s fixed point theorem for directional contractions.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
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