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

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## Abstract

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## Preview

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© Akadémiai Kiadó, Budapest, Hungary 2012