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Generalizations of Caristi-Kirk’s theorem on partial metric spaces. (English) Zbl 1281.54027

Summary: In this article, lower semi-continuous maps are used to generalize Caristi-Kirk’s fixed point theorem on partial metric spaces. First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize it to complete partial metric spaces. Some more general results are also obtained in partial metric spaces.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces
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