Determination of conjugate means by reducing to the generalized Matkowski–Sutô equation
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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
Key words and phrasesmean functional equation quasi-arithmetic mean conjugate mean
Mathematics Subject Classification26E60 39B22
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© Akadémiai Kiadó, Budapest, Hungary 2012