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On Latif’s fixed point theorems. (English) Zbl 1241.54031

Some generalized fixed point theorems for the w-distance were given in [A. Latif, “Generalized Caristi’s fixed point theorems”, Fixed Point Theory Appl. 2009, Article ID 170140 (2009; Zbl 1171.54031)]. In the paper under review, it is proved that Latif’s fixed point statements are equivalent with some weak-distance variants of Caristi’s fixed point statement, Ekeland’s variational principle statement and Takahashi’s nonconvex minimization statement.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
54C60 Set-valued maps in general topology
47H10 Fixed-point theorems
49J53 Set-valued and variational analysis

Citations:

Zbl 1171.54031
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