Contractions on probabilistic metric spaces: examples and counterexamples.
- Autores: B. Schweizer, Howard Sherwood, Robert M. Tardiff
- Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 12, Nº. 1, 1988, págs. 5-17
- Idioma: inglés
- Títulos paralelos:
- Contracciones en espacios métricos probabilísticos: ejemplos y contraejemplos.
- Enlaces
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Resumen
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,tW) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger spaces under Min and similar t-norms, the contractions of Sehgal and Bharucha-Reid are also ordinary contractions on related metric spaces.
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