Abstract
We deal with the functional equations
for \({x, y \in [0, \infty)}\), \({x \geq y}\), where \({f : [0, \infty) \to \mathbb{R}}\) and \({\sigma, \tau : [0, \infty)\to [0, 1]}\); and
for \({x, y \in \mathcal{C}}\), \({x - y \in \mathcal{C}}\), where \({\mathcal{C}}\) is a convex cone in a real linear space, \({F : \mathcal{C} \to \mathbb{R}}\) and \({\sigma, \tau : \mathcal{C} \to [0, 1]}\). We determine the solutions of these equations satisfying some natural regularity assumptions. In this way we generalize the result of J. Aczél and R. D. Luce.
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References
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Chudziak, J. On functional equation stemming from utility theory and psychophysics. Aequat. Math. 89, 355–365 (2015). https://doi.org/10.1007/s00010-014-0297-z
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DOI: https://doi.org/10.1007/s00010-014-0297-z