Displaying similar documents to “On the relationship between Menger spaces and Wald spaces”

Caristi's fixed point theorem in probabilistic metric spaces

Kianoush Fathi Vajargah, Hamid Mottaghi Golshan, Abbas Arjomand Far (2021)

Kybernetika

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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.

Contractions on probabilistic metric spaces: examples and counterexamples.

Berthold Schweizer, Howard Sherwood, Robert M. Tardiff (1988)

Stochastica

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The notion of a contraction mapping for a probabilistic metric space recently introduced by T. L. Hicks is compared with the notion previously introduced by V. L. Sehgal and A. T. Bharucha-Reid. By means of appropriate examples, it is shown that these two notions are independent. It is further shown that every Hick's contraction on a PM space (S,F,t) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger...