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Smooth convex $ t$-norms do not exist


Authors: C. Alsina and M. S. Tomás
Journal: Proc. Amer. Math. Soc. 102 (1988), 317-320
MSC: Primary 39B05,; Secondary 26A51
DOI: https://doi.org/10.1090/S0002-9939-1988-0920993-8
MathSciNet review: 920993
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Abstract: We show that smooth convex $ t$-norms do not exist.


References [Enhancements On Off] (What's this?)

  • [1] J. Aczél, Lectures on functional equations and their applications, Mathematics in Science and Engineering, Vol. 19, Academic Press, New York-London, 1966. Translated by Scripta Technica, Inc. Supplemented by the author. Edited by Hansjorg Oser. MR 0208210
  • [2] Claudi Alsina, On countable products and algebraic convexifications of probabilistic metric spaces, Pacific J. Math. 76 (1978), no. 2, 291–300. MR 506132
  • [3] C. Alsina and B. Schweizer, The countable product of probabilistic metric spaces, Houston J. Math. 9 (1983), no. 3, 303–310. MR 719088
  • [4] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1934.
  • [5] Cho-hsin Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965), 189–212. MR 0190575
  • [6] B. Schweizer and A. Sklar, Probabilistic metric spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York, 1983. MR 790314

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0920993-8
Article copyright: © Copyright 1988 American Mathematical Society

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