The space of probabilistic 1-Lipschitz maps View Full Text


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Article Info

DATE

2019-03-21

AUTHORS

Mohammed Bachir

ABSTRACT

We introduce and study the natural notion of probabilistic 1-Lipschitz maps. We use the space of all probabilistic 1-Lipschitz maps to give a new method for the construction of probabilistic metric completion (respectively of probabilistic invariant metric group completion). Our construction is of independent interest. We prove that the space of all probabilistic 1-Lipschitz maps defined on a probabilistic invariant metric group can be endowed with a monoid structure. Next, we explicit the set of all invertible elements of this monoid and characterize probabilistic invariant complete Menger groups by the space of all probabilistic 1-Lipschitz maps in the spirit of the classical Banach–Stone theorem. More... »

PAGES

1-29

References to SciGraph publications

  • 2000. Triangular Norms in NONE
  • 1971-06. Complete probabilistic metric spaces in PROBABILITY THEORY AND RELATED FIELDS
  • 2001. Fixed Point Theory in Probabilistic Metric Spaces in NONE
  • 1993-08. On the definition of a probabilistic normed space in AEQUATIONES MATHEMATICAE
  • 2018-05. Well Posedness and Inf-Convolution in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2009-03. A Mazur–Ulam theorem for probabilistic normed spaces in AEQUATIONES MATHEMATICAE
  • Journal

    TITLE

    Aequationes mathematicae

    ISSUE

    N/A

    VOLUME

    N/A

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00010-019-00641-0

    DOI

    http://dx.doi.org/10.1007/s00010-019-00641-0

    DIMENSIONS

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