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On Heuvers’ Logarithmic Functional Equation

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Abstract

ƒ(x + y) - ƒ(x) - ƒ(y) = ƒ(x −1 + y −l) are identical to those of the Cauchy equation ƒ(xy) = ƒ(x) + ƒ(y) when ƒ is a function from the positive real numbers into the reals. In the present article, we prove this equivalence for functions mapping the set of nonzero elements of a field (excluding ℤ2) .

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References

  1. Heuvers, K.J., Another logarithmic functional equation, Aequationes Math. 58 (1999), 260–264.

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  1. Department of Mathematics & Statistics, Mississippi State University, P.O. Box MA, Mississippi State, MS, 39762, USA

    Bruce R. Ebanks

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  1. Bruce R. Ebanks
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Correspondence to Bruce R. Ebanks.

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Ebanks, B.R. On Heuvers’ Logarithmic Functional Equation. Results. Math. 42, 37–41 (2002). https://doi.org/10.1007/BF03323552

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  • DOI: https://doi.org/10.1007/BF03323552

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