Contractions on probabilistic metric spaces: examples and counterexamples.

Schweizer, 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 -