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Maximal and minimal point theorems and Caristi’s fixed point theorem. (English) Zbl 1304.54085

Summary: This study is concerned with the existence of fixed points of Caristi-type mappings motivated by a problem stated by Kirk. First, several existence theorems of maximal and minimal points are established. By using them, some generalized Caristi’s fixed point theorems are proved, which improve Caristi’s fixed point theorem and the results in the studies of Jachymski, Feng and Liu, Khamsi, and Li.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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References:

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