Abstract
We discuss the functional equation
where I is a nonvoid open subinterval of the set of real numbers ℝ, f: I→ℝ is an unknown function, and M, N are weighted quasi-arithmetic means on I. Our typical assumption will be that M and N are comparable. Complete solution will be presented under the additional supposition that f is the product of the generating functions of M and N, respectively.
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This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK81402 and by the TÁMOP 4.2.1./B-09/1/KONV-2010-0007 project implemented through the New Hungary Development Plan co-financed by the European Social Fund, and the European Regional Development Fund.
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Daróczy, Z., Maksa, G. A functional equation involving comparable weighted quasi-arithmetic means. Acta Math Hung 138, 147–155 (2013). https://doi.org/10.1007/s10474-012-0221-8
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DOI: https://doi.org/10.1007/s10474-012-0221-8