Variants of the new caristi theorem

HIGHLIGHTS

SUMMARY

There have appeared two types of generalizations of the original Caristi fixed point theorem on complete metric spaces. Motivated by Example 4.1 of_[6], the authors derive the following from Theorem D: Theorem F. Let (X, d) be a metric space and a proper function φ: X → R be l.s.c. from above and bounded from below (resp. u.s.c. from below and bounded from above). From his own principle, Takahashi deduced Caristi`s fixed point theorem, Ekeland`s ε-variational principle, Nadler`s fixed point theorem, etc. From Theorem F(α), (γ) and the . . .

 



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