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De Rham systems and the solution of a class of functional equations

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Summary

The main objective of this paper is to solve the functional equation

$$N(f_0 (x)) = f_1 (N(x))$$

with strong negationN as unknown function. From the solution of a system of functional equations studied by De Rham in 1956, we obtain the unique solution of our equation and, from a convenient dense set in [0, 1], a description of the key function is attained. As application, we present a class of binary operations on [0, 1] which is stable byN-duality if, and only if,N is the solution of the above equation.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of the Balearic Islands, E-07071, Palma de Mallorca, Spain

    G. Mayor & J. Torrens

Authors
  1. G. Mayor
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  2. J. Torrens
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Mayor, G., Torrens, J. De Rham systems and the solution of a class of functional equations. Aeq. Math. 47, 43–49 (1994). https://doi.org/10.1007/BF01838138

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  • DOI: https://doi.org/10.1007/BF01838138

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