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Cauchy's equation on Δ+: Further results

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Summary

In a previous paper [Cauchy's equation on Δ +, Aequationes Math.41 (1991), 192–211], we began the study of Cauchy's equation on Δ+, the space of probability distribution functions of nonnegative random variables. In this paper we continue this study and extend our previous results to triangle functions of the formτ T, L , whereT is a continuous Archimedean t-norm andL a binary operation onR +, which is iseomorphic to a strict t-conorm. We again use a lattice theoretic approach, and introduce first a theorem on the powers and roots of certain elements of Δ+ underτ T,L . Under certain additional restrictions we obtain a representation of sup-continuous solutions, similar to the one found in the first paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA

    Thomas Riedel

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  1. Thomas Riedel
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Riedel, T. Cauchy's equation on Δ+: Further results. Aeq. Math. 44, 236–248 (1992). https://doi.org/10.1007/BF01830982

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  • DOI: https://doi.org/10.1007/BF01830982

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