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Keywords:
probabilistic metric space; Caristi's fixed point; Archimedean t-norm
Summary:
In this work, we define a partial order on probabilistic metric spaces and establish some new Caristi's fixed point theorems and Ekeland's variational principle for the class of (right) continuous and Archimedean t-norms. As an application, a partial answer to Kirk's problem in metric spaces is given.
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