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A functional equation involving comparable weighted quasi-arithmetic means

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Abstract

We discuss the functional equation

$$f(M(x,y))=f(N(x,y)) \qquad (x,y\in I) $$

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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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, H-4010, Debrecen, Pf. 12, Hungary

    Zoltán Daróczy & Gyula Maksa

Authors
  1. Zoltán Daróczy
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  2. Gyula Maksa
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Corresponding author

Correspondence to Zoltán Daróczy.

Additional information

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

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