# Contractions on probabilistic metric spaces: examples and counterexamples.

Berthold Schweizer; Howard Sherwood; Robert M. Tardiff

Stochastica (1988)

- Volume: 12, Issue: 1, page 5-17
- ISSN: 0210-7821

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topSchweizer, Berthold, Sherwood, Howard, and Tardiff, Robert M.. "Contractions on probabilistic metric spaces: examples and counterexamples.." Stochastica 12.1 (1988): 5-17. <http://eudml.org/doc/39008>.

@article{Schweizer1988,

abstract = {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.},

author = {Schweizer, Berthold, Sherwood, Howard, Tardiff, Robert M.},

journal = {Stochastica},

keywords = {Espacios métricos; Espacios probabilísticos; Aplicación contractiva; Estudio comparativo; fixed point; Menger space; simple space; probabilistic contractions},

language = {eng},

number = {1},

pages = {5-17},

title = {Contractions on probabilistic metric spaces: examples and counterexamples.},

url = {http://eudml.org/doc/39008},

volume = {12},

year = {1988},

}

TY - JOUR

AU - Schweizer, Berthold

AU - Sherwood, Howard

AU - Tardiff, Robert M.

TI - Contractions on probabilistic metric spaces: examples and counterexamples.

JO - Stochastica

PY - 1988

VL - 12

IS - 1

SP - 5

EP - 17

AB - 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.

LA - eng

KW - Espacios métricos; Espacios probabilísticos; Aplicación contractiva; Estudio comparativo; fixed point; Menger space; simple space; probabilistic contractions

UR - http://eudml.org/doc/39008

ER -