Aequationes mathematicae

, Volume 84, Issue 1–2, pp 77–90 | Cite as

The equality problem in the class of conjugate means

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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
$$M(x,y):=\varphi^{-1}(p\varphi(x)+q\varphi(y)+(1-p-q)\varphi(L(x,y)))=:L_\varphi^{(p,q)}(x,y),$$
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.

Mathematics Subject Classification (2000)

Primary 39B22 Secondary 39B12 26E60 

Keywords

Mean functional equation quasi-arithmetic mean conjugate mean 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Faculty of InformaticsUniversity of DebrecenDebrecenHungary
  2. 2.Department of MathematicsTU BerlinBerlinGermany
  3. 3.Mathematics Research UnitUniversity of LuxembourgLuxembourgGrand Duchy of Luxembourg

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