Abstract
The class of quasi-arithmetic means and the class of Beckenbach–Gini means are essentially different. The problem of characterization of the means which belong to both classes leads to a composite functional equation for two unknown functions. We solve this functional equation assuming that a generator of quasi-arithmetic mean is once continuously differentiable.
Mathematics Subject Classification (1991): Primary 30B12, 26E60
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Matkowski, J. (2011). On Means Which are Quasi-Arithmetic and of the Beckenbach–Gini Type. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_37
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DOI: https://doi.org/10.1007/978-1-4614-0055-4_37
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