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Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups

  • T. M. G. Ahsanullah EMAIL logo and Gunther Jäger
Published/Copyright: July 14, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 4

Abstract

We define probabilistic convergence groups based on Tardiff’s neighborhood systems for probabilistic metric spaces and develop the basic theory. We study, as natural examples, probabilistic metric groups and probabilistic normed groups as well as probabilistic limit groups under a t-norm as defined earlier by the authors. We further show that a probabilistic convergence group induces a natural probabilistic uniform convergence structure and give a result on probabilistic metrization.

MSC 2010: Primary 54A20; 54B30; 54E15; 54E36; 54E70; 54H11
Keywords: probabilistic metric space; distance distribution function; profile function; Tardiff-neighborhood system; probabilistic convergence space; probabilistic uniform convergence space; probabilistic convergence group; probabilistic uniformization; probabilistic metric group; probabilistic normed group; probabilistic metrization; category theory

(Communicated by Anatolij Dvurečenskij)

Acknowledgement

We are sincerely thankful to both the referees for their scrupulous checking of our previous manuscript, and offering various useful suggestions including some interesting references which led to an improvement of this paper. We also thank the area editor Professor Anatolij Dvurečenskij for his kind support.

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Received: 2015-4-13
Accepted: 2016-4-11
Published Online: 2017-7-14
Published in Print: 2017-8-28

© 2017 Mathematical Institute Slovak Academy of Sciences

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  4. Hamiltonian ordered algebras and congruence extension
  6. Automorphism groups with some finiteness conditions
  8. Only finitely many Tribonacci Diophantine triples exist
  10. Abundant semigroups with a *-normal idempotent
  12. Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses
  14. Monotonicity results for delta fractional differences revisited
  16. M-Cantorvals of Ferens type
  18. Comparison of ψ-porous topologies
  20. On certain generalized matrix methods of convergence in (ℓ)-groups
  22. Some applications of first-order differential subordinations
  24. Hankel determinant for a class of analytic functions involving conical domains defined by subordination
  26. Nonoscillation and exponential stability of the second order delay differential equation with damping
  28. Positive solutions of perturbed nonlinear hammerstein integral equation
  30. Ricci solitons on 3-dimensional cosymplectic manifolds
  32. Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups
  34. The super socle of the ring of continuous functions
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  38. Finiteness of the discrete spectrum in a three-body system with point interaction
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https://doi.org/10.1515/ms-2017-0027
Keywords for this article
probabilistic metric space; distance distribution function; profile function; Tardiff-neighborhood system; probabilistic convergence space; probabilistic uniform convergence space; probabilistic convergence group; probabilistic uniformization; probabilistic metric group; probabilistic normed group; probabilistic metrization; category theory

Articles in the same Issue

  2. Outer measure on effect algebras
  4. Hamiltonian ordered algebras and congruence extension
  6. Automorphism groups with some finiteness conditions
  8. Only finitely many Tribonacci Diophantine triples exist
  10. Abundant semigroups with a *-normal idempotent
  12. Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses
  14. Monotonicity results for delta fractional differences revisited
  16. M-Cantorvals of Ferens type
  18. Comparison of ψ-porous topologies
  20. On certain generalized matrix methods of convergence in (ℓ)-groups
  22. Some applications of first-order differential subordinations
  24. Hankel determinant for a class of analytic functions involving conical domains defined by subordination
  26. Nonoscillation and exponential stability of the second order delay differential equation with damping
  28. Positive solutions of perturbed nonlinear hammerstein integral equation
  30. Ricci solitons on 3-dimensional cosymplectic manifolds
  32. Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups
  34. The super socle of the ring of continuous functions
  36. On the internal approach to differential equations 2. The controllability structure
  38. Finiteness of the discrete spectrum in a three-body system with point interaction
  40. On a subclass of Bazilevic functions
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