## Abstract

Let \({I\subset\mathbb{R}}\) be a nonempty open interval and let \({L:I^2\to I}\) be a fixed strict mean. A function \({M:I^2\to I}\) is said to be an *L-conjugate mean on I* if there exist \({p,q\in{]}0,1]}\) and a strictly monotone and continuous function *φ* such that

for all \({x,y\in I}\) . Here *L*(*x*, *y*) is a fixed quasi-arithmetic mean. We will solve the equality problem in this class of means.

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This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK 81402 (first and second author) and OTKA “Mobility” call HUMAN-MB08A-84581 (first author).

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Burai, P., Dascăl, J. The equality problem in the class of conjugate means.
*Aequat. Math.* **84**, 77–90 (2012). https://doi.org/10.1007/s00010-011-0113-y

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DOI: https://doi.org/10.1007/s00010-011-0113-y