LAUSR

Given a continuous strictly monotone function $$\varphi $$φ defined on an open real interval I and a probability measure $$\mu $$μ on the Borel subsets of [0, 1], the Makó–Páles mean is defined by $$\begin{aligned} {\mathcal {M}}_{\varphi ,\mu }(x,y):=\varphi ^{-1}\left( \int ^1_0\varphi (tx+(1-t)y)\, d\mu (t)\right) ,\quad x,y\in I. \end{aligned}$$Mφ,μ(x,y):=φ-1∫01φ(tx+(1-t)y)dμ(t),x,y∈I.Under some conditions on the functions $$\varphi $$φ and $$\psi $$ψ defined on I, the quotient mean is given by $$\begin{aligned} Q_{\varphi ,\psi }(x,y):=\left( \frac{\varphi }{\psi }\right) ^{-1}\left( \frac{\varphi (x)}{\psi (y)}\right) , \quad x,y\in I. \end{aligned}$$Qφ,ψ(x,y):=φψ-1φ(x)ψ(y),x,y∈I.In this paper, we study some invariance of the quotient mean with respect to Makó–Páles means.