Acta Mathematica Hungarica

, Volume 139, Issue 1–2, pp 1–10 | Cite as

Determination of conjugate means by reducing to the generalized Matkowski–Sutô equation

  • Justyna JarczykEmail author


Given a weighted quasi-arithmetic mean L on an interval I we find all conjugate means derived from L which are weighted quasi-arithmetic, that is we determine all numbers p,q∈(0,1] and continuous strictly monotonic functions φ: I→ℝ such that the mean given by is weighted quasi-arithmetic. Some special cases of the problem were solved by Z. Daróczy, Zs. Páles, Gy. Maksa and J. Dascăl.

Key words and phrases

mean functional equation quasi-arithmetic mean conjugate mean 

Mathematics Subject Classification

26E60 39B22 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics, Computer Science and EconometricsUniversity of Zielona GóraZielona GóraPoland

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